7th Grade Cross-Sections of Three-Dimensional Figures Test Solutions and Scoring (PDF)

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

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

Use this answer key and scoring guide to grade the cross-sections test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

Grade 7 · Common Core State Standards: 7.G.A.3

Grade 7 cross sections test answers: worked solutions

Question 1 – Prism slice [2 pts]

A cut parallel to the base is a rectangle congruent to the base: 10 by 4.

\(10\times 4=40\)

Rectangle 10 by 4; area 40

The cross-section.

Scoring: 1 point for the shape and dimensions; 1 point for the area.

Question 2 – Vertical slice [2 pts]

The cross-section is a 5-by-7 rectangle.

\(5\times 7=35\)

Rectangle; 35 square centimeters

Scoring: 1 point for the shape; 1 point for the area.

Question 3 – Pyramid slice [2 pts]

\(\frac{10-4}{10}\times 12=\frac{36}{5}=7.2\) units.

\(7.2^{2}=51.84\)

Side 7.2; area 51.84

Scoring: 1 point for the side length; 1 point for the area.

Question 4 – Through the apex [2 pts]

A triangle with base 10 and height 14.

\(A=\frac{1}{2}(10)(14)=70\)

Triangle; area 70

Scoring: 1 point for the shape; 1 point for the area.

Question 5 – Name the slice [2 pts]

Square.
Triangle.
Rectangle.

Square; triangle; rectangle

Scoring: Half a point per correct answer; round up.

Question 6 – Area comparison [2 pts]

The remaining fraction is \(\frac{2}{3}\), so the side is \(\frac{2}{3}\times 12=8\).

\(8^{2}=64\)

64 square inches

Scoring: 1 point for the side; 1 point for the area.

Question 7 – Storage box [2 pts]

The surface is 16 in by 12 in: \(192\) square inches.

\(192\times 6=1152\)

192 square inches; 1,152 cubic inches

Scoring: 1 point for the area; 1 point for the volume.

Question 8 – Two cuts [3 pts]

Side \(\frac{2}{3}\times 6=4\); area \(16\).
Triangle with base 6 and height 9: \(\frac{1}{2}(6)(9)=27\).
Plane B, by \(27-16=11\).

Results.

Scoring: 1 point for each part.

Question 9 – Cube cuts [3 pts]

Square, \(6\times 6=36\) square inches.
Triangle.
A parallel plane meets four faces, so the cross-section has four sides, not three.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this grade 7 cross sections test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 7 chapters: Grade 7 math.

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