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

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

Cover of the book Grade 7 Math Worksheets with Answers (PDF)

Download as a PDFThe Grade 7 worksheets book with answersPrintable PDFSee the book ›

Sommaire

This circles practice solutions 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 to check your work on the circles worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

Grade 7 · Common Core State Standards: 7.G.B.4

Circles practice solutions: exercises 1 to 10

Exercise 1 – Circumference from diameter

$C=\pi d=3.14\times 10=31.4$

31.4 inches (exactly $10\pi$ in)

Exercise 2 – Circumference from radius

$C=2\pi r=2\times 3.14\times 7=43.96$

43.96 feet

Exercise 3 – Area from radius

$A=\pi r^{2}=3.14\times 25=78.5$

78.5 square centimeters

Exercise 4 – Area from diameter

Radius: $12\div 2=6$.

$A=3.14\times 6^{2}=3.14\times 36=113.04$

113.04 square inches

Exercise 5 – Radius from circumference

$r=C\div(2\pi)=18.84\div 6.28=3$

radius 3 ft; diameter 6 ft

Exercise 6 – Radius from area

$r^{2}=50.24\div 3.14=16$, so $r=4$.

4 meters

Exercise 7 – Pi as 22/7

$C=2\times\frac{22}{7}\times 14=88$.

$A=\frac{22}{7}\times 14^{2}=\frac{22}{7}\times 196=616$

88 cm; 616 square centimeters

Exercise 8 – Semicircle perimeter

Curved part: $\frac{1}{2}\times 3.14\times 10=15.7$.

Add the diameter: $15.7+10=25.7$

25.7 inches

Exercise 9 – Quarter circle

$\frac{1}{4}\times 3.14\times 8^{2}=\frac{1}{4}\times 200.96=50.24$

50.24 square inches

Exercise 10 – In terms of pi

$C=\pi d=9\pi$.

Radius is $\frac{9}{2}$, so $A=\pi\left(\frac{9}{2}\right)^{2}=\frac{81}{4}\pi$

$9\pi$ m; $\frac{81}{4}\pi$ square meters

Exercises 11 and up

Exercise 11 – Bike wheel

One turn = circumference: $3.14\times 26=81.64$ in.

Ten turns: $81.64\times 10=816.4$

81.64 inches; 816.4 inches

Exercise 12 – Two pizzas

Small: $3.14\times 6^{2}=113.04$.

Large: $3.14\times 8^{2}=200.96$.

$200.96-113.04=87.92$

113.04 and 200.96 square inches; the large has 87.92 more

Pizza areas.

Exercise 13 – Composite figure

Rectangle: $10\times 6=60$.

Semicircle radius 3: $\frac{1}{2}\times 3.14\times 9=14.13$.

$60+14.13=74.13$

74.13 square feet

Area parts.

Exercise 14 – Ring

Outer: $3.14\times 64=200.96$. Inner: $3.14\times 25=78.5$.

$200.96-78.5=122.46$

122.46 square millimeters (exactly $39\pi$)

Exercise 15 – Garden fence

$C=2\times 3.14\times 6=37.68$ ft.

$37.68\times 3.50=131.88$

37.68 feet; $131.88

Exercise 16 – Round table

Radius: 2.5 ft.

$3.14\times 2.5^{2}=3.14\times 6.25=19.625\approx 19.63$

19.63 square feet

The area steps.

Exercise 17 – Running track

One lap: $3.14\times 100=314$ yd.

$3\times 314=942$

942 yards

Exercise 18 – Circle in a square

The circle has radius 5: $3.14\times 25=78.5$.

Square: $10\times 10=100$.

$100-78.5=21.5$

21.5 square inches

Exercise 19 – Pie crust

$3.14\times 4.5^{2}=3.14\times 20.25=63.585\approx 63.59$

63.59 square inches

Exercise 20 – Clock hand

In one hour the tip goes once around a circle of radius 6 in.

$C=2\times 3.14\times 6=37.68$

37.68 inches

Key facts behind this circles practice solutions

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 practice solutions

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the circles practice solutions as a PDF with the button below and keep it with your notes.

All Grade 7 chapters: Grade 7 math.

Voter.. post

Free printable PDF