7th Grade Circumference and Area of Circles Test Solutions and Scoring (PDF)

7th Grade math test solutions: Circumference and Area of Circles – Maths PDF

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This circles test answers for 7th Grade covers circumference and area of circles (Common Core 7.G.B.4), with a free PDF to print.

Use this answer key and scoring guide to grade the circles 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.4

Circles test answers: worked solutions

Question 1 – Circumference [2 pts]

\(C=\pi d=\frac{22}{7}\times 14=44\)

44 inches

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

Question 2 – Area [2 pts]

\(A=3.14\times 9^{2}=3.14\times 81=254.34\)

254.34 square centimeters

Steps.

Scoring: 1 point for squaring the radius; 1 point for the answer.

Question 3 – Find the radius [2 pts]

\(r=62.8\div 6.28=10\) ft.

\(A=3.14\times 100=314\)

radius 10 ft; area 314 square feet

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

Question 4 – Leave it in pi [2 pts]

\(C=2\pi(12)=24\pi\).

\(A=\pi(12)^{2}=144\pi\)

\(24\pi\) m; \(144\pi\) square meters

Scoring: 1 point for each.

Question 5 – Semicircle [2 pts]

Perimeter: \(\frac{1}{2}(3.14)(20)+20=31.4+20=51.4\) cm.

Area: \(\frac{1}{2}(3.14)(10^{2})=157\)

51.4 cm; 157 square centimeters

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

Question 6 – Wheel distance [2 pts]

One turn: \(2\times 3.14\times 15=94.2\) in.

\(5\times 94.2=471\)

471 inches

Scoring: 1 point for the circumference; 1 point for 5 turns.

Question 7 – Leftover metal [2 pts]

Square: \(20\times 20=400\). Circle: \(3.14\times 100=314\).

\(400-314=86\)

86 square inches

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

Question 8 – Track [3 pts]

Straight sides: 80 m; the two semicircles make one circle: \(3.14\times 20=62.8\); total \(142.8\) m.
Rectangle \(40\times 20=800\) plus circle \(3.14\times 10^{2}=314\): \(1114\) square meters.
\(5\times 142.8=714\) m.

Results.

Scoring: 1 point for each part.

Question 9 – Rug with a hole [3 pts]

\(3.14\times 100=314\) square units.
\(3.14\times 36=113.04\) square units.
\(314-113.04=200.96\) square units.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this circles test answers

Key facts

Diameter \(d = 2r\); radius is half the diameter.
Circumference \(C = \pi d = 2\pi r\).
Area \(A = \pi r^2\) (square the radius first).
\(\pi\) is about \(3.14\) or \(\frac{22}{7}\); leave answers in terms of pi to be exact.
A semicircle has half the area of the circle; its perimeter adds the diameter.

How to use this circles 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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