7th Grade Area, Volume and Surface Area Test Solutions and Scoring (PDF)

7th Grade math test solutions: Area, Volume and Surface Area – Maths PDF

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This area volume surface area test answers for 7th Grade covers area, volume and surface area (Common Core 7.G.B.6), with a free PDF to print.

Use this answer key and scoring guide to grade the volume and surface area 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.B.6

Area volume surface area test answers: worked solutions

Question 1 – Triangle [2 pts]

\(A=\frac{1}{2}\times 15\times 8=60\)

60 square centimeters

Scoring: 1 point for the formula; 1 point for the answer.

Question 2 – Trapezoid [2 pts]

\(A=\frac{1}{2}(7+13)(6)=60\)

60 square meters

Scoring: 1 point for the formula; 1 point for the answer.

Question 3 – Prism volume and surface [2 pts]

\(V=8\times 5\times 4=160\).

\(SA=2(40)+2(32)+2(20)=80+64+40=184\)

160 cubic inches; 184 square inches

The net has six rectangles.

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

Question 4 – Triangular prism [2 pts]

Base area: \(\frac{1}{2}\times 6\times 8=24\).

\(V=24\times 9=216\)

216 cubic inches

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

Question 5 – Composite figure [2 pts]

\(12\times 9=108\), \(3\times 4=12\).

\(108-12=96\)

96 square feet

Scoring: 1 point for the two areas; 1 point for the difference.

Question 6 – Missing height [2 pts]

Height: \(150\div 30=5\) cm.

Surface area: \(2(30)+2(30)+2(25)=60+60+50=170\)

5 cm; 170 square centimeters

Scoring: 1 point for the height; 1 point for the surface area.

Question 7 – Pool water [2 pts]

\(25\times 10\times 3=750\) cubic feet.

Full pool: \(25\times 10\times 4=1000\). \(750\div 1000=75\%\)

750 cubic feet; 75%

Scoring: 1 point for the volume of water; 1 point for the percent.

Question 8 – Net [3 pts]

A rectangular prism that is 5 by 3 by 2.
\(2(15)+2(10)+2(6)=30+20+12=62\) square units.
\(5\times 3\times 2=30\) cubic units.

Surface area table.

Scoring: 1 point for each part.

Question 9 – Wedge of cheese [3 pts]

\(\frac{1}{2}\times 6\times 4=12\) square inches.
\(12\times 12=144\) cubic inches.
\(144\times 0.05=7.20\) dollars.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this area volume surface area test answers

Key facts

Triangle: \(A = \frac{1}{2} bh\). Trapezoid: \(A = \frac{1}{2} (b_1 + b_2) h\).
Composite polygon: add the areas of simple pieces or subtract a missing piece.
Volume of a prism: \(V = Bh\) (base area times height).
Surface area of a prism: add the areas of all faces from the net.
Area uses square units; volume uses cubic units.

How to use this area volume surface area 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.

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