7th Grade Cross-Sections of Three-Dimensional Figures Test with Point Values (PDF)

7th Grade math test: Cross-Sections of Three-Dimensional Figures – Maths PDF

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This grade 7 cross sections test for 7th Grade covers cross-sections of three-dimensional figures (Common Core 7.G.A.3), with a free PDF to print.

This 45-minute test checks the two-dimensional shapes made when planes slice right rectangular prisms and right rectangular pyramids, including slices parallel and perpendicular to a base (Common Core 7.G.A.3). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Cross-Sections of Three-Dimensional Figures
Standards: 7.G.A.3
Time: 45 minutes
Total: 20 points

Grade 7 cross sections test: questions

Question 1 – Prism slice [2 pts]

A prism cut parallel to its base.

Name the shape of the cross-section and find its dimensions and area.

Question 2 – Vertical slice [2 pts]

A prism is 9 cm long, 5 cm deep, and 7 cm tall. A vertical plane parallel to the 5-by-7 side face cuts it. Name the shape and find its area.

Question 3 – Pyramid slice [2 pts]

A square pyramid cut parallel to the base.

Find the side length and area of the square cross-section.

Question 4 – Through the apex [2 pts]

A vertical cut through the apex.

Name the shape of the cross-section and find its area.

Question 5 – Name the slice [2 pts]

Name the cross-section in each case. (a) A cube is cut parallel to a face. (b) A square pyramid is cut by a plane through the apex perpendicular to the base. (c) A rectangular prism is cut by a plane parallel to the base.

Question 6 – Area comparison [2 pts]

A square pyramid has a base of 12 in. A plane parallel to the base cuts it at one-third of the way to the apex from the base. Find the area of the cross-section.

Question 7 – Storage box [2 pts]

A storage box is a prism 16 in long, 12 in wide, and 10 in tall. It is filled to a depth of 6 in with sand. Find the area of the sand’s surface and the volume of the sand.

Question 8 – Two cuts [3 pts]

Two planes cut the same pyramid.

Find the side and area of the cross-section made by plane A. (1 point)
Find the shape and area of the cross-section made by plane B. (1 point)
Which cross-section has the greater area? By how much? (1 point)

Question 9 – Cube cuts [3 pts]

A cube with edges of 6 inches.

A plane parallel to a face cuts the cube. Name the shape and find the area. (1 point)
A plane cuts off a corner by meeting three faces. Name the shape. (1 point)
Explain why a plane parallel to a face of a cube can never give a triangle. (1 point)

Key facts behind this grade 7 cross sections test

Key facts

A cross-section is the flat shape where a plane meets a solid.
Prism slice parallel to a face: a rectangle congruent to that face.
Pyramid slice parallel to the base: a smaller rectangle similar to the base.
Pyramid slice through the apex and perpendicular to the base: a triangle.
A slanted plane can give a triangle, trapezoid, or other polygon.

How to use this grade 7 cross sections test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

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