HSG.GMD.B.4: Cross-Sections and Solids of Revolution
In plain English: HSG.GMD.B.4 is the Common Core geometry standard that asks students to identify the two-dimensional shape made when a plane slices a three-dimensional object, and the solid formed when a flat figure is rotated about a line. For example, slicing a cylinder parallel to its base gives a circle, and spinning a rectangle about one side makes a cylinder. It is usually taught in high school Geometry.
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Common Core State Standards for Mathematics · Domain: Geometric Measurement and Dimension (GMD) · Cluster: Visualize relationships between two-dimensional and three-dimensional objects Also written as HSG-GMD.B.4 or G-GMD.4 · Official standard
This lesson builds two kinds of spatial reasoning. First, students predict and name the flat shape where a plane cuts a solid: a cube, a prism, a pyramid, a cylinder, a cone or a sphere, cut parallel to the base, perpendicular to it or on a slant. Second, they run the process the other way around a line: a flat figure spun 360° about an axis sweeps out a solid, and students name that solid and read its radius and height from the figure.
Students slice clay models and spin paper shapes on a pencil, so every claim can be tested by hand. Where a size is asked for, they use similar triangles or the Pythagorean Theorem to give the dimensions of the cross-section or of the solid.
Learning Objectives
By the end of this lesson, students will be able to:
Identify the cross-sections of prisms, pyramids, cylinders, cones and spheres made by planes parallel to the base, perpendicular to it or slanted
Explain why some shapes cannot be cross-sections of a given solid, for example why a cube has no seven-sided or circular cross-section
Identify the solid generated when a rectangle, right triangle, semicircle, trapezoid or circle is rotated about a line, and give its radius and height
Work backward from a solid to a two-dimensional figure and axis that would generate it
Prior Knowledge Required
Students should already be comfortable with:
Plane sections of right rectangular prisms and pyramids 7.G.A.3
Names and parts of prisms, pyramids, cylinders, cones and spheres 7.G.B.6
Show a roll of cookie dough (a cylinder) and an orange (close to a sphere). Students sketch their answers alone for three minutes, then compare with a partner.
Warm-Up Prompt
"You slice a roll of cookie dough straight across, then lengthwise through the middle, then on a slant. Sketch the cut face each time. Then slice an orange anywhere with one straight cut. What shape is the cut face? Does it depend on where you cut?"
The dough gives a circle, a rectangle and an ellipse (an oval). The orange always gives a circle; only its size changes, and the largest circle comes from a cut through the center. Record the words "cross-section" and "plane" on the board and keep the sketches for Direct Instruction.
Direct Instruction20 minutes
Part 1: Cross-sections. A cross-section is the flat shape where a plane meets a solid. Its shape depends on the solid and on how the plane is tilted. Build the table with the class, testing each cell on a clay model or in geometry software.
Cross-sections by solid and plane direction
Solid
Plane parallel to the base
Plane perpendicular to the base
Slanted plane
Cube or rectangular prism
Rectangle congruent to the base (a square for a cube)
Rectangle
Triangle, quadrilateral, pentagon or hexagon, depending on the tilt
Square pyramid
Smaller square
Isosceles triangle (through the apex) or trapezoid (not through the apex)
Triangle, quadrilateral or pentagon
Cylinder
Circle congruent to the base
Rectangle
Ellipse if the plane misses both bases
Cone
Smaller circle
Isosceles triangle (through the apex)
Ellipse if the plane crosses only the curved surface
Sphere
Circle
Circle
Circle
Two ideas explain the table. Each side of a polygon cross-section lies on one face of the solid, so a cube (6 faces) can give at most a hexagon. And a cut parallel to the base of a pyramid or cone gives a figure similar to the base, scaled by the fraction of the height that remains above the cut. Use Diagram 1 for the four cube sections.
Part 2: Solids of revolution. When a flat figure is rotated 360° about a line in its plane (the axis), every point traces a circle centered on the axis. Use Diagram 2.
Rectangle about one of its sides: a cylinder. The side on the axis is the height; the other side is the radius.
Right triangle about a leg: a cone. The leg on the axis is the height, the other leg is the radius, and the hypotenuse becomes the slant height.
Semicircle about its diameter: a sphere with the same radius.
Figure not touching the axis: a hole appears. A rectangle beside the axis gives a tube (a cylinder with a cylindrical hole), and a circle beside the axis gives a torus (a donut shape).
Figure with the axis along a slanted side: check every vertex. A right triangle spun about its hypotenuse gives two cones joined at their bases.
Cube cut through three corners
A plane passes through three vertices of a cube with edge 6 cm that are all joined by edges to the same vertex. What is the cross-section?
Equation: An equilateral triangle; each side is a face diagonal, 6√2 ≈ 8.49 cm
Cone cut parallel to the base
A cone has base radius 6 cm and height 12 cm. A plane parallel to the base cuts it 4 cm above the base. What is the cross-section?
Equation: A circle; by similar triangles its radius is 6 · 8/12 = 4 cm
Sphere cut off-center
A plane cuts a sphere of radius 10 cm at a distance of 6 cm from the center. What is the cross-section?
Equation: A circle with radius √(10² - 6²) = 8 cm
Right triangle about a leg
A right triangle with legs 5 cm and 12 cm is rotated about the 12 cm leg. What solid is formed?
Equation: A cone with radius 5 cm, height 12 cm and slant height 13 cm
Rectangle beside the axis
A 3 cm by 7 cm rectangle is rotated about a line parallel to its 7 cm sides, 2 cm from the nearer side. What solid is formed?
Equation: A tube: a cylinder of radius 5 cm and height 7 cm with a cylindrical hole of radius 2 cm
Guided Practice15 minutes
Pairs answer on whiteboards and justify each answer with a sketch. (a) A cylinder with radius 4 cm and height 10 cm is cut by a plane that contains its axis. (A rectangle 8 cm by 10 cm.) (b) A square pyramid is cut by a plane parallel to its base halfway up. (A square with half the base edge.) (c) A semicircle with radius 3 is rotated about its diameter. (A sphere with radius 3.) (d) A right trapezoid with parallel sides 2 cm and 5 cm and a 4 cm leg perpendicular to them is rotated about that leg. (A frustum, a cone with its top cut off, with radii 2 cm and 5 cm and height 4 cm.) Listen for these errors: giving the radius as the diameter, calling the solid from a rectangle a "prism", and drawing only the half of the solid that the figure sweeps first.
Independent Practice15 minutes
Students work alone on five items. (1) Name the cross-section of a cone made by a plane that is perpendicular to the base and passes through the apex (an isosceles triangle). (2) A cube with edge 4 cm is cut by a plane through two opposite edges; name the section and give its dimensions (a rectangle 4 cm by 4√2 ≈ 5.66 cm). (3) A 6 cm by 2 cm rectangle is rotated about a 2 cm side; name the solid (a cylinder with radius 6 cm and height 2 cm). (4) A circle of radius 1 whose center is 3 units from a line in its plane is rotated about that line (a torus). (5) A right triangle with legs 6 and 8 is rotated about its hypotenuse (two cones joined at a shared base of radius 6 · 8/10 = 4.8).
Closure5-10 minutes
Exit ticket: (1) An isosceles triangle is rotated about its line of symmetry. Name the solid and sketch it (a cone). (2) Name two different cross-sections of a triangular prism and describe the plane that makes each one (a triangle, parallel to the bases; a rectangle, parallel to a lateral face). (3) Explain in one sentence why a sphere never has a square cross-section.
Differentiation Strategies
For Struggling Students
Keep clay models and a paper-on-pencil spinner on the desk for every problem, and let students test before they answer
Give a partly filled cross-section table and ask students to complete one row at a time
For rotations, have students first reflect the figure across the axis on paper, then connect the matching points with ellipses
For Advanced Students
Find a plane that cuts a cube in a rhombus that is not a square, and describe it by the points where it meets the edges
Explain why a regular pentagon cannot be a cross-section of a cube, using the fact that the cube has only three pairs of parallel faces
Rotate the region between the lines y = x and y = 2 for 0 ≤ x ≤ 2 about the y-axis and describe the solid (a cone)
Assessment Guidance
What to Look For
Listen for the direction of the plane (parallel, perpendicular, slanted) and the position of the axis in every answer: "a triangle" without "through the apex" is incomplete. Good sketches show the plane meeting each face or the curved surface. For rotations, strong answers name the solid and say which part of the figure becomes the radius and which the height. Watch for students who call the solid from a rectangle a prism, who give the diameter as the radius, or who miss the hole when the figure does not touch the axis.
02
Classroom Activities
3 Activities
1
Clay Slicing Lab
20 minGroups of 3
Groups mold solids from clay and slice them with dental floss. Pressing each cut face onto paper and tracing it gives a record of the cross-section that students can compare with their predictions.
Procedure
Mold a cube, a cylinder, a cone and a square pyramid, each about 5 cm across
Before each cut, write a prediction. Then cut with floss parallel to the base, perpendicular to the base and on a slant, and trace each cut face
Remold the cube and try to make a triangle, a pentagon and a hexagon. Record where the floss entered and left the cube for each one
Mold a ball and cut it twice, once near the edge and once through the middle. Compare the two circles
Discussion Questions
Could any cut of the cube give a circle? A seven-sided shape? Explain using the faces of the cube
Which solid gave the same shape for every cut? Why?
How did a slanted cut of the cylinder change when it crossed one of the flat bases?
Modification for Distance Learning
Students use a free 3D geometry tool to intersect a plane with each solid, drag the plane through different tilts, and paste screenshots of five different cross-sections into a shared slide.
2
Spin It
15 minPairs
Pairs tape cardstock shapes to a pencil and spin the pencil quickly between their palms. The blur shows the solid of revolution, and students record its name and dimensions.
The 6 Shapes
Shape 1: a 3 cm by 5 cm rectangle taped along a 5 cm side (a cylinder, r = 3 cm, h = 5 cm)
Shape 2: a right triangle with legs 4 cm and 6 cm taped along the 6 cm leg (a cone, r = 4 cm, h = 6 cm)
Shape 3: a semicircle of radius 4 cm taped along its diameter (a sphere, r = 4 cm)
Shape 4: the same right triangle taped along its hypotenuse (two cones joined at their bases)
Shape 5: a 2 cm by 5 cm rectangle held 1 cm away from the pencil by a paper strip (a tube with inner radius 1 cm and outer radius 3 cm)
Shape 6: a paper circle of radius 1.5 cm with its center held 3 cm from the pencil (a torus)
Procedure
Before each spin, predict the solid and sketch it
Spin, observe, and record the solid's name, radius and height
For Shape 4, find the radius of the shared base (hypotenuse √52 ≈ 7.2 cm, radius 4 · 6 ÷ √52 ≈ 3.3 cm)
Challenge Variation
Each pair designs a new flat shape that spins into a solid shaped like a pencil with a sharpened tip (a cylinder topped by a cone), then trades with another pair, who must predict the solid before spinning.
3
Cross-Section Match-Up
20 minGroups of 3-4
Groups match 8 description cards (a solid and a plane) to 8 shape cards, then explain each match to another group. The set is built so that every shape card is used exactly once.
The 8 Description Cards and Their Matches
A cylinder cut by a plane that contains its axis: rectangle
A sphere cut by a plane that misses the center: circle smaller than the sphere's great circle
A cube cut through the three vertices joined to one corner: equilateral triangle
A cube cut through its center by a plane perpendicular to a long diagonal: regular hexagon
A square pyramid cut parallel to its base: square
A square pyramid cut by a vertical plane parallel to a base edge that misses the apex: trapezoid
A cylinder cut by a slanted plane that misses both bases: ellipse
A cube cut by a plane that crosses five of its faces: pentagon
Procedure
Shuffle both sets and deal them face up. Match each description with a shape card and sketch the plane on a picture of the solid
When all 8 are matched, each group writes two new description cards for a solid and a plane of its choice and trades them with another group
Modification for a Shorter Class
Use only the four cube and pyramid cards and do the rest as a whole-class discussion with a clay model.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Four Cross-Sections of a Cube
The same cube cut four ways, in an oblique view (dashed edges are hidden). A plane parallel to a face gives a square; a plane through two opposite edges gives a rectangle s by s√2; a plane through three corners gives an equilateral triangle with side s√2; and a plane through the center perpendicular to a long diagonal passes through the midpoints of six edges and gives a regular hexagon with side s√2/2. The shapes look slanted in the drawing, but these are their true shapes.
Diagram 2: Solids Generated by Rotations
Drawn to scale. Rotating a 3 by 5 rectangle about its 5-unit side gives a cylinder with radius 3 and height 5. Rotating a right triangle with legs 3 and 5 about the 5-unit leg gives a cone with radius 3 and height 5. Rotating a semicircle of radius 3 about its diameter gives a sphere of radius 3.
04
Homework Assignment
~30 min
HSG.GMD.B.4 Homework: Cross-Sections and Solids of Revolution
Directions: For every problem, make a sketch that shows the plane or the axis. Name each shape or solid, give its dimensions where asked, and explain your reasoning in a sentence.
Part 1: Cross-Sections (Problems 1-3)
A box is a right rectangular prism 8 cm long, 5 cm wide and 3 cm tall, resting on its 8 cm by 5 cm face. Name the cross-section and give its dimensions for (a) a horizontal plane, (b) a vertical plane parallel to the 8 cm by 3 cm faces, and (c) a vertical plane through two diagonally opposite vertical edges (give the length to the nearest hundredth).
A cone has base radius 9 cm and height 12 cm. (a) Name the cross-section made by a plane parallel to the base 8 cm above it, and find its radius. (b) Name the cross-section made by a plane perpendicular to the base through the apex, and give its side lengths. (c) Explain why no cross-section of a cone can be a square.
A sphere has radius 13 cm. (a) A plane cuts it 5 cm from the center. Name the cross-section and find its radius. (b) Where must the plane be to give the largest possible cross-section, and what is its radius? (c) A cube is cut by a plane. Explain why the cross-section can never have seven sides.
Part 2: Solids of Revolution (Problems 4-6)
A rectangle is 4 cm by 9 cm. (a) Name the solid formed by rotating it about a 9 cm side, and give its radius and height. (b) Do the same for a rotation about a 4 cm side. (c) Which solid is wider, and how much wider across?
A right triangle has legs 7 cm and 24 cm and hypotenuse 25 cm. Name the solid and give its dimensions when the triangle is rotated about (a) the 24 cm leg, (b) the 7 cm leg, and (c) the hypotenuse. For (c), find the radius of the shared base and the height of each part.
Name and describe the solid formed by rotating (a) a semicircle of radius 5 about its diameter, (b) a quarter circle of radius 5 about one of its straight edges, and (c) a circle of radius 2 about a line in its plane that is 6 units from its center. For (c), give the inner and outer radius of the solid.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Identification
Every shape and solid named correctly
One or two names wrong
Most names wrong or missing
Sketches
Plane or axis shown clearly on every sketch
Sketches present but plane or axis unclear
No sketches
Dimensions
Radii, heights and side lengths correct, with units
Minor errors, such as a diameter given as a radius
Dimensions missing or wrong
Reasoning
Clear explanations for the "why" parts (squares in cones, seven-sided sections)
Explanations incomplete
No explanations
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Choose an answer for each multiple-choice question and work the short-answer questions on paper before opening the solution. Your score updates as you go, and Reset quiz starts over.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A cylinder is cut by a plane parallel to its bases. What is the cross-section?
Answer: B
A plane parallel to the bases gives a circle congruent to each base. Choice A comes from a plane perpendicular to the bases, and choice C from a slanted plane.
Question 2 of 20 · Multiple Choice
A square pyramid is cut by a plane parallel to its base. What is the cross-section?
Answer: D
A cut parallel to the base gives a figure similar to the base, so a smaller square. Choice A comes from a vertical cut through the apex, and choice B from a vertical cut that misses the apex.
Question 3 of 20 · Multiple Choice
A sphere is cut by a plane that does not pass through its center. What is the cross-section?
Answer: A
Every plane section of a sphere is a circle. Only a plane through the center gives a circle with the sphere's radius (a great circle), so an off-center cut gives a smaller one. Choice B is a common guess from drawings, where circles look like ovals in perspective.
Question 4 of 20 · Multiple Choice
A cone is cut by a slanted plane that crosses the curved surface all the way around without touching the base. What is the cross-section?
Answer: C
A tilted closed cut of a cone gives an ellipse. Choice A needs the plane to be parallel to the base, and choice B needs a plane through the apex.
Question 5 of 20 · Multiple Choice
Which shape can NOT be a cross-section of a cube?
Answer: D
Each side of a cross-section lies on a different face of the cube, and a cube has only 6 faces, so a section has at most 6 sides. Triangles, pentagons and hexagons are all possible, so choices A, B and C can occur.
Question 6 of 20 · Multiple Choice
A triangular prism is cut by a plane parallel to one of its rectangular faces (and between that face and the opposite edge). What is the cross-section?
Answer: A
The plane meets each triangular base in a segment parallel to one side and meets the prism along its whole length, so the section is a rectangle. Choice B comes from a plane parallel to the triangular bases.
Question 7 of 20 · Multiple Choice
A plane cuts a sphere of radius 17 cm at a distance of 8 cm from the center. What is the radius of the circular cross-section?
Answer: B
The sphere's radius, the distance to the plane and the circle's radius form a right triangle with the sphere's radius as hypotenuse: r = √(17² - 8²) = √225 = 15 cm. Choice A subtracts 17 - 8, and choice C adds the squares instead of subtracting.
Question 8 of 20 · Multiple Choice
A rectangle is rotated 360° about one of its sides. What solid is formed?
Answer: C
Each point of the opposite side traces a circle, so the solid has two circular bases and a curved side: a cylinder. Choice D confuses the rectangle's flat faces with the result of a rotation, which always has circular cross-sections perpendicular to the axis.
Question 9 of 20 · Multiple Choice
A right triangle with legs 8 cm and 15 cm is rotated about the 15 cm leg. Which describes the solid?
Answer: B
The leg on the axis (15 cm) is the height, and the other leg (8 cm) is the radius. The hypotenuse, √(8² + 15²) = 17 cm, is the slant height. Choice A swaps radius and height, and choice C uses the slant height as the height.
Question 10 of 20 · Multiple Choice
A circle of radius 4 is rotated about a line that contains one of its diameters. What solid is formed?
Answer: C
Each half of the circle is a semicircle on the axis, and a semicircle rotated about its diameter sweeps out a sphere with the same radius. Choice D needs a circle that does not touch the axis.
Question 11 of 20 · Multiple Choice
A rectangle is rotated about a line in its plane that is parallel to one of its sides and 3 cm away from the rectangle. What solid is formed?
Answer: D
The gap between the axis and the rectangle sweeps out empty space, so the solid is a tube (like a pipe). Choice A would need the rectangle to touch the axis, and choice B needs a circle, not a rectangle.
Question 12 of 20 · Multiple Choice
An isosceles triangle is rotated about its base (the side between the two equal sides). What solid is formed?
Answer: A
The apex opposite the base traces a circle, and each half of the triangle is a right triangle rotating about a leg, so each half makes a cone and the two cones share a base. Choice B is the result of rotating about the line of symmetry instead.
Question 13 of 20 · Multiple Choice
Which rotation generates a cylinder with radius 2 cm and height 6 cm?
Answer: A
The side on the axis becomes the height (6 cm) and the other side becomes the radius (2 cm). Choice B gives radius 6 cm and height 2 cm, choice C gives radius 6 cm and height 4 cm, and choice D gives a cone.
Question 14 of 20 · Multiple Choice
A cylinder with radius 5 cm and height 9 cm is cut by a plane that contains its axis. What is the cross-section?
Answer: C
The plane cuts straight through the middle, so the rectangle's width is the diameter, 2 · 5 = 10 cm, and its height is 9 cm. Choice A uses the radius instead of the diameter.
Question 15 of 20 · Short Answer
A cube with edge 10 cm is cut by a plane parallel to one face, 3 cm from that face. Name the cross-section and give its dimensions.
A square 10 cm by 10 cm. Every plane parallel to a face of a cube gives a square congruent to the face, whatever its distance from the face.
Question 16 of 20 · Short Answer
A square pyramid has base edge 12 cm and height 9 cm. A plane parallel to the base cuts it 6 cm above the base. Name the cross-section and find its side length.
A square. The part above the cut is a smaller pyramid of height 9 - 6 = 3 cm, similar to the whole with scale factor 3/9 = 1/3, so the side is 12 · 1/3 = 4 cm.
Question 17 of 20 · Short Answer
A plane starts parallel to the bases of a cylinder and slowly tilts until it is perpendicular to them, always passing through the center of the cylinder. Describe how the cross-section changes.
It starts as a circle. As the plane tilts it becomes an ellipse, which gets longer while the plane still misses both bases. Once the plane crosses the bases, the section is cut off by two straight segments, and when the plane is perpendicular to the bases it is a rectangle.
Question 18 of 20 · Short Answer
A 3 cm by 8 cm rectangle is rotated about one of its 8 cm sides. The solid is then cut by a plane that contains the axis. Name the solid and the cross-section, with dimensions.
The solid is a cylinder with radius 3 cm and height 8 cm. The cross-section through the axis is the rectangle together with its mirror image across the axis: a rectangle 6 cm by 8 cm.
Question 19 of 20 · Short Answer
Describe a two-dimensional figure and an axis that would generate a cone with radius 6 cm and height 8 cm.
A right triangle with legs 6 cm and 8 cm, rotated about the 8 cm leg. The hypotenuse, √(6² + 8²) = 10 cm, becomes the slant height of the cone.
Question 20 of 20 · Short Answer
A square with side 4 cm is rotated about one of its diagonals. Describe the solid and give its dimensions.
Two congruent cones joined at their bases. The diagonal is 4√2 ≈ 5.66 cm long, and the other two vertices are half a diagonal, 2√2 ≈ 2.83 cm, from it. So each cone has radius 2√2 cm and height 2√2 cm.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSG.GMD.B.4 mean?
HSG.GMD.B.4 means students can name the flat shape made when a plane slices a solid, and name the solid made when a flat figure is rotated about a line. For example, a cone sliced parallel to its base gives a circle, and a right triangle rotated about a leg gives a cone.
Is HSG.GMD.B.4 taught in Geometry?
Yes, HSG.GMD.B.4 is usually taught in high school Geometry, often in the unit on volume and three-dimensional figures. It builds on 7.G.A.3, where students slice right rectangular prisms and pyramids, and adds cylinders, cones, spheres and rotations.
What is a cross-section in geometry?
A cross-section is the two-dimensional shape where a plane meets a three-dimensional solid. Its shape depends on the solid and on the direction of the plane: a cylinder gives a circle when cut parallel to its bases and a rectangle when cut through its axis.
What cross-sections can a cube have?
A cube can have triangles, quadrilaterals (squares, rectangles, trapezoids and others), pentagons and hexagons as cross-sections. It cannot have a polygon with more than six sides, because each side lies on one of the six faces, and it cannot have a circle, because all its faces are flat.
What are the cross-sections of a cone?
A cone gives a circle when cut parallel to the base, an ellipse when cut on a slant through the curved surface only, and an isosceles triangle when cut through the apex perpendicular to the base. Other cuts give regions bounded by parabolas and hyperbolas; those curves, the conic sections, are studied later in Algebra II or Precalculus.
What is a solid of revolution?
A solid of revolution is the solid swept out when a flat figure turns 360° about a line in its plane, called the axis. A rectangle about a side makes a cylinder, a right triangle about a leg makes a cone, and a semicircle about its diameter makes a sphere.
How do you find the solid made by rotating a shape?
Reflect the figure across the axis, then imagine every point tracing a circle around the axis. The distance of a point from the axis is the radius of its circle. If the figure touches the axis along a side, the solid is solid there; if there is a gap, the solid has a hole.
What mistakes do students make with cross-sections and rotations?
A frequent mistake is calling the solid from a rotated rectangle a prism instead of a cylinder. Others are giving the figure's width as the diameter instead of the radius, missing the hole when the figure does not touch the axis, and naming a cross-section without saying which direction the plane cuts.
How does HSG.GMD.B.4 connect to later math?
HSG.GMD.B.4 prepares students for Cavalieri's principle (HSG.GMD.A.2), which compares volumes by comparing cross-sections, and for calculus, where volumes of solids of revolution are found by adding up thin circular slices. Engineers and medical imaging (CT scans) also build 3D pictures from cross-sections.
How can students practice visualizing cross-sections at home?
Slice fruit, cheese or modeling clay in different directions and trace the cut faces, or tape paper shapes to a pencil and spin it. Free 3D geometry apps also let students drag a plane through a solid and watch the cross-section change.
07
Related Standards
5 standards
These standards connect to HSG.GMD.B.4: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
7.G.A.3Prerequisite
Describe the 2D figures made by slicing prisms and pyramids
