Answer Keys: Circumference & Area of Circles

Student Concept Worksheet Answers

1

C = 16pi cm OR C = 50.24 cm

C = 2 x pi x 8 = 16pi = 16 x 3.14 = 50.24 cm

2

C = 14pi in OR C = 43.96 in

C = pi x 14 = 14pi = 14 x 3.14 = 43.96 in

3

A = 36pi sq m OR A = 113.04 sq m

A = pi x 6 squared = pi x 36 = 36pi = 36 x 3.14 = 113.04 sq m

4

A = 100pi sq ft OR A = 314 sq ft

r = 20/2 = 10 ft. A = pi x 10 squared = pi x 100 = 100pi = 100 x 3.14 = 314 sq ft

5

C = 18pi ft OR C = 56.52 ft of fencing

Fencing = circumference. C = pi x 18 = 18pi = 18 x 3.14 = 56.52 ft

6

A = 16pi sq m OR A = 50.24 sq m

Area covered. A = pi x 4 squared = pi x 16 = 16pi = 16 x 3.14 = 50.24 sq m

Practice Worksheet Answers

Part A: Find the Circumference

#	Answer	Work
1	18pi cm = 56.52 cm	C = 2 x pi x 9 = 18pi
2	16pi in = 50.24 in	C = pi x 16 = 16pi
3	22pi m = 69.08 m	C = 2 x pi x 11 = 22pi
4	25pi ft = 78.5 ft	C = pi x 25 = 25pi

Part B: Find the Area

#	Answer	Work
5	16pi sq cm = 50.24 sq cm	A = pi x 4 squared = 16pi
6	100pi sq in = 314 sq in	A = pi x 10 squared = 100pi
7	16pi sq m = 50.24 sq m	r = 4, A = pi x 4 squared = 16pi
8	49pi sq ft = 153.86 sq ft	r = 7, A = pi x 7 squared = 49pi

Part C: Find Both

9

C = 12pi = 37.68 in | A = 36pi = 113.04 sq in

C = 2 x pi x 6 = 12pi. A = pi x 36 = 36pi.

10

C = 22pi = 69.08 cm | A = 121pi = 379.94 sq cm

C = pi x 22 = 22pi. r = 11, A = pi x 121 = 121pi.

Part D: Word Problems

11

37.68 feet of tile trim

C = pi x 12 = 12 x 3.14 = 37.68 ft

12

153.86 square inches

A = pi x 7 squared = 3.14 x 49 = 153.86 sq in

13

r = 4 feet

50.24 = 3.14 x r squared. r squared = 50.24/3.14 = 16. r = 4 ft

14

d = 24 inches

75.36 = 3.14 x d. d = 75.36/3.14 = 24 in

15

$109.90

C = 2 x 3.14 x 5 = 31.4 m. Cost = 31.4 x $3.50 = $109.90

16

$904.32

r = 12 ft. A = 3.14 x 144 = 452.16 sq ft. Cost = 452.16 x $2 = $904.32

Part E: Challenge

17

25.7 cm

Half circumference = (3.14 x 10)/2 = 15.7 cm. Add straight edge = 10 cm. Total = 25.7 cm

18

4 times larger

A of Circle A = pi x 9 = 9pi. A of Circle B = pi x 36 = 36pi. 36pi / 9pi = 4

FAST Practice Quiz Answers

1

B) 50.24 cm

C = 2 x pi x r = 2 x 3.14 x 8 = 50.24 cm. A is half (using just pi x r). C is area. D ignores pi.

2

B) 113.04 square inches

r = 12/2 = 6. A = pi x 6 squared = 3.14 x 36 = 113.04 sq in. A is circumference. C uses diameter instead of radius. D is just d squared.

3

B) 10 meters

C = pi x d. 31.4 = 3.14 x d. d = 31.4/3.14 = 10 m. A is the radius.

4

Select: "The diameter is twice the radius," "Area is measured in square units," "Circumference and perimeter mean the same thing for circles"

The diameter is twice the radius - TRUE (d = 2r)
The circumference formula uses radius squared - FALSE (area uses r squared)
Area is measured in square units - TRUE
If you double the radius, the area doubles - FALSE (area quadruples because r is squared)
Circumference and perimeter mean the same thing for circles - TRUE

5

B) 31.40 feet

Fencing = circumference. C = 2 x pi x r = 2 x 3.14 x 5 = 31.4 ft. A uses just pi x r. C and D are area-related.

6

B) 5 feet

A = pi x r squared. 78.5 = 3.14 x r squared. r squared = 78.5/3.14 = 25. r = 5 ft.

FAST Quiz Scoring Guide

Score	Interpretation	Recommended Action
6/6	Mastery	Ready for composite figures and more complex applications
4-5/6	Approaching Mastery	Review specific errors - radius/diameter confusion or formula selection
2-3/6	Developing	Reteach with hands-on activities - measuring actual circles
0-1/6	Needs Intervention	Small group instruction on basic circle vocabulary and formula meaning

Common Error Patterns to Watch For: