Spectrum Math Grade 7 Chapter 5 Lesson 6 Answer Key Circles: Area

This handy Spectrum Math Grade 7 Answer Key Chapter 5 Lesson 5.6 Circles: Area provides detailed answers for the workbook questions

Spectrum Math Grade 7 Chapter 5 Lesson 5.6 Circles: Area Answers Key

To find the area of a circle, use the formula A = π × r². Remember, the radius (r) is half the diameter. It is the distance from the center of the circle to its outer edge.

Find the area of each circle below. Use 3.14 for π. Round your answer to the nearest tenth.

Question 1.
a.

_____________ square feet
Answer:
50.2 sq. ft.

Explanation:
Given,
Diameter = 8 ft.
We know that,
π = 3.14 or 22/7
Radius = d/2
r = 8/2
r = 4 ft.
A = π × r²
A = 3.14 x 4 x 4
A = 50.24 sq. ft.

b.

_____________ square meters
Answer:
113 sq. m.

Explanation:
Given,
Diameter = 12 m.
We know that,
π = 3.14 or 22/7
Radius = d/2
r = 12/2
r = 6 ft.
A = π × r²
A = 3.14 x 6 x 6
A = 113.04 sq. m.

c.

_______________ square centimeters
Answer:
530.7 sq. cm.

Explanation:
We know that,
π = 3.14 or 22/7
Given,
Radius = 13 cm.
A = π × r²
A = 3.14 x 13 x 13
A = 530.7 sq. cm.

Question 2.
a.

_______________ square yards
Answer:
1,1017.4 sq. yd.

Explanation:
Given,
Diameter = 36 yd.
We know that,
π = 3.14 or 22/7
Radius = d/2
r = 36/2
r = 18 ft.
A = π × r²
A = 3.14 x 18 x 18
A = 1,1017.4 sq. yd.

b.

_______________ square kilometers
Answer:
452.2 sq. km.

Explanation:
We know that,
π = 3.14 or 22/7
Given,
Radius = 12 km
A = π × r²
A = 3.14 x 12 x 12
A =  452.16 or 452.2 sq. ft.

c.

_______________ square inches
Answer:
153.9 sq. in.

Explanation:
We know that,
π = 3.14 or 22/7
Given,
Radius = 7 in.
A = π × r²
A = 3.14 x 7 x 7
A = 153.86 or 153.9 sq. ft.

Complete the chart for each circle described below. Use 3.14 for π. When necessary, round to the nearest tenth.

Question 3.
a. Diameter: ____________ inches
b. Radius: 3 inches
c. Area: ____________ square inches
Answer:
a. Diameter: 6 inches.
c. Area: 28.3 square inches.

Explanation:
Given,
Radius = 3 inches.
Diameter = 2r
D = 2 x 3
D = 6 inches.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 3 x 3
A = 28.26 or 28.3 sq. in.

Question 4.
a. Diameter: 18 feet
b. Radius: ____________ feet
c. Area: ____________ square feet
Answer:
b. Radius: 9 feet.
c. Area: 254.3 square feet.

Explanation:
Given,
Diameter = 18 ft.
Radius = d/2
R = 18/2
R = 9 ft.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 9 x 9
A = 254.34 or 254.3 sq. ft.

Question 5.
a. Diameter: 17 meters
b. Radius: ____________ meters
c. Area: ____________ square meters
Answer:
b. Radius: 8.5 meters.
c. Area: 226.9 square meters.

Explanation:
Given,
Diameter = 17 m
Radius = d/2
r = 17/2
r = 8.5 m
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 8.5 x 8.5
A = 226.865 or 226.9 sq. m.

Question 6.
a. Diameter: ____________ centimeters
b. Radius: 32 centimeters
c. Area: ____________ square centimeters
Answer:
a. Diameter: 64 centimeters.
c. Area: 3,215.4 square centimeters.

Explanation:
Given,
Radius = 32 inches.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 32 x 32
A = 3,215.36 or 3,215.4 sq. in.

Complete the chart for each circle described below. Use 3.14 for π. When necessary, round to the nearest hundredth.

Question 1.
a. Radius: 4 in.
b. Diameter: ____________ in.
c. Area: ____________ in.²
Answer:
b. Diameter: 8 in.
c. Area: 50.24 in.²

Explanation:
Given,
Radius = 4 inches.
Diameter = 2r
D = 2 x 4 = 8 inches.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 4 x 4
A =  50.24 sq. in.

Question 2.
a. Radius: ____________ ft.
b. Diameter: 12 ft.
c. Area: ____________ ft.²
Answer:
a. Radius: 6 ft.
c. Area: 113.04 ft.²

Explanation:
Given,
Diameter = 12ft
Radius = d/2
R = 12/2
R = 6 ft.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 6 x 6
A = 113.04 sq. ft.

Question 3.
a. Radius: 1.5 m
b. Diameter: ____________ m
c. Area: ____________ m²
Answer:
b. Diameter: 3 m
c. Area: 7.07 m²

Explanation:
Given,
Radius = 1.5 m.
Diameter = 2r
D = 2 x 1.5
D = 3 m.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 1.5 x 1.5
A = 7.065 or 7.07 sq. m.

Question 4.
a. Radius: 11 in.
b. Diameter: ____________ in.
c. Area: ____________ in.²
Answer:
b. Diameter: 22 in.
c. Area: 379.94 in.²

Explanation:
Given,
Radius = 11 inches.
Diameter = 2r
D = 2 x 11
D = 22 inches.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 11 x 11
A = 379.94 sq. in.

Question 5.
a. Radius: ____________ km
b. Diameter: 0.8 km
c. Area: ____________ km²
Answer:
a. Radius: 0.4 km
c. Area: 0.50 km²

Explanation:
Given,
Diameter = 0.8 km.
Radius = d/2
r = 0.8/2
r = 0.4 km
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 0.4 x 0.4
A = 0.5024 or 0.50 sq. km.

Question 6.
a. Radius: 90 mm
b. Diameter: ____________ mm
c. Area: ____________ mm²
Answer:
b. Diameter: 180 mm
c. Area: 25,434 mm²

Explanation:
Given,
Radius = 90 mm
Diameter = 2r
D = 2 x 90
D = 180 mm
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 90 x 90
A = 25,434 sq. mm.

Question 7.
a. Radius: 5 ft.
b. Diameter: ____________ ft.
c. Area: ____________ ft.²
Answer:
b. Diameter: 10 ft.
c. Area: 78.5 ft.²

Explanation:
Given,
Radius =5 ft
Diameter = 2r
D = 2 x 5
D = 10 ft
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 5 x 5
A = 78.5 sq. ft.

Question 8.
a. Radius: ____________ in.
b. Diameter: 9 in.
c. Area: ____________ in.²
Answer:
a. Radius: 4.5 in.
c. Area: 63.59 in.²

Explanation:
Given,
Diameter = 9 in.
Radius = d/2
r = 9/2
r = 4.5 in.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 4.5 x 4.5
A = 63.585 or 63.59 sq. in.

Question 9.
a. Radius: ____________ cm
b. Diameter: 8.2 cm
c. Area: ____________ cm²
Answer:
a. Radius: 4.1cm
c. Area: 52.78 cm²

Explanation:
Given,
Diameter = 8.2 cm
Radius = d/2
r = 8.2/2
r = 4.1 cm
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 4.1 x 4.1
A = 52.7834 or 52.78 sq. cm.

Question 10.
a. Radius: ____________ m
b. Diameter: 11 m
c. Area: ____________ m²
Answer:
a. Radius: 5.5 m
c. Area: 94.99 m²

Explanation:
Given,
Diameter = 11 m
Radius = d/2
r = 11/2
r = 5.5 m
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 5.5 x 5.5
A = 94.985 or 94.99 sq. m.

Question 11.
a. Radius: 3 cm
b. Diameter: ____________ cm
c. Area: ____________ cm²
Answer:
b. Diameter: 6 cm
c. Area: 28.26 cm²

Explanation:
Given,
Radius = 3 cm
Diameter = 2r
D = 2 x 3
D = 6 cm
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 3 x 3
A = 28.26 sq. cm.

Question 12.
a. Radius: 12 in.
b. Diameter: ____________ in.
c. Area: ____________ in.²
Answer:
b. Diameter: 24 in.
c. Area: 452.16 in.²

Explanation:
Given,
Radius = 12 inches.
Diameter = 2r
D = 2 x 12
D = 24 inches.
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 12 x 12
A = 452.16 sq. in.

Question 13.
a. Radius: ____________ km
b. Diameter: 28 km
c. Area: ____________ km²
Answer:
a. Radius: 14 km
c. Area: 615.44 km²

Explanation:
Given,
Diameter = 28 km
Radius = d/2
r = 28/2
r = 14 km
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 14 x 14
A = 615.44 sq. km.

Question 14.
a. Radius: 9 m
b. Diameter: ____________ m
c. Area: ____________ m²
Answer:
b. Diameter: 18 m
c. Area: 254.34 m²

Explanation:
Given,
Radius = 9 m
Diameter = 2r
D = 2 x 9
D = 18 m
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 9 x 9
A = 254.34 sq. m.

Question 15.
a. Radius: ____________ cm
b. Diameter: 22 cm
c. Area: ____________ cm²
Answer:
a. Radius: 11 cm
c. Area: 379.94 cm²

Explanation:
Given,
Diameter = 22 cm
Radius = d/2
r = 22/2
r = 11 cm
A = π × r²
We know that,
π = 3.14 or 22/7
A = 3.14 x 11 x 11
A = 379.94 sq. cm.

Find the area for each circle below. Use 3.14 for π. When necessary, round to the nearest hundredth.

Question 1.
a.

_____________ m²
Answer:
197.46 m²

Explanation:
Given,
Radius = 7.93 m, π = 3.14
A = π × r²
A = 3.14 x 7.93 x 7.93
A = 197.458 or 197.46 sq. m.

b.

_____________ cm²
Answer:
21.23 cm²

Explanation:
Given,
Diameter = 5.2 cm, π = 3.14
Radius = d/2
r = 5.2/2
r = 2.6 cm
A = π × r²
A = 3.14 x 2.6 x 2.6
A = 21.226 or 21.23 sq. cm.

c.

_____________ in.²
Answer:
60.79 in²

Explanation:
Given,
Radius = 4.4 in, π = 3.14
A = π × r²
A = 3.14 x 4.4 x 4.4
A = 60.7904 or 60.79 sq. in.

Question 2.
a.

_____________ km²
Answer:
19.63 km²

Explanation:
Given,
Diameter = 5 km, π = 3.14
Radius = d/2
r = 5/2
r = 2.5 km
A = π × r²
A = 3.14 x 2.5 x 2.5
A = 19.625 or 19.63 sq. km.

b.

______________ ft.²
Answer:
3.80 ft²

Explanation:
Given,
Radius = 1.1 ft, π = 3.14
A = π × r²
A = 3.14 x 1.1 x 1.1
A = 3.79 or 3.80 sq. ft.

c.

______________ m²
Answer:
706.5 m²

Explanation:
Given,
Radius = 15 m, π = 3.14
A = π × r²
A = 3.14 x 15 x 15
A = 706.5 sq. m.

Question 3.
a.

______________ yd.²
Answer:
32.15 yd²

Explanation:
Given,
Radius = 3.2 yd, π = 3.14
A = π × r²
A = 3.14 x 3.2 x 3.2
A = 32.153 or 32.15 sq. yd.

b.

______________ cm²
Answer:
15.90 cm²

Explanation:
Given,
Diameter = 4.5 cm, π = 3.14
Radius = d/2
r = 4.5/2
r = 2.25 cm
A = π × r²
A = 3.14 x 2.25 x 2.25
A = 15.896 or 15.90 sq. cm.

c.

______________ mm²
Answer:
1,319.59 m²

Explanation:
Given,
Diameter = 41 mm, π = 3.14
Radius = d/2
r = 41/2
r = 20.5 mm
A = π × r²
A = 3.14 x 20.5 x 20.5
A = 1,319.585 or 1,319.59 sq. m.

Question 4.
a.

______________ m²
Answer:
8.76 m²

Explanation:
Given,
Diameter = 3.34 m, π = 3.14
Radius = d/2
r = 3.34/2
r = 1.67 m
A = π × r²
A = 3.14 x 1.67 x 1.67
A = 8.757 or 8.76 sq. m.

b.

_______________ cm²
Answer:
28.26 cm²

Explanation:
Given,
Radius = 3 cm, π = 3.14
A = π × r²
A = 3.14 x 3 x 3
A = 28.26 sq. cm.

c.

_______________ in.²
Answer:
100.24 in²

Explanation:
Given,
Radius = 5.65 in, π = 3.14
A = π × r²
A = 3.14 x 5.65 x 5.65
A = 100.236 or 100.24 sq. in.

Question 5.
a.

_______________ cm²
Answer:
10.63 cm²

Explanation:
Given,
Diameter = 3.68 cm, π = 3.14
Radius = d/2
r = 3.68/2
r = 1.84 cm
A = π × r²
A = 3.14 x 1.84 x 1.84
A = 10.6307 or 10.63 sq. cm.

b.

_______________ in.²
Answer:
452.16 in²

Explanation:
Given,
Radius = 12 in, π = 3.14
A = π × r²
A = 3.14 x 12 x 12
A = 452.16 sq. in.

c.

_______________ ft.²
Answer:
10.75 m²

Explanation:
Given,
Diameter = 3.7 ft, π = 3.14
Radius = d/2
r = 3.7/2
r = 1.85 ft
A = π × r²
A = 3.14 x 1.85 x 1.85
A = 10.746 or 10.75 sq. m.

Question 6.
a.

_______________ mi.²
Answer:
0.03 mi²

Explanation:
Given,
Radius = 0.09 mi, π = 3.14
A = π × r²
A = 3.14 x 0.09 x 0.09
A = 0.0254 or 0.03 sq. mi.

b.

________________ yd.²
Answer:
1,533.61 yd²

Explanation:
Given,
Diameter = 44.2 yd, π = 3.14
Radius = d/2
r = 44.2/2
r = 22.1 yd
A = π × r²
A = 3.14 x 22.1 x 22.1
A = 1,533.6074 or 1,533.61 sq. yd.

c.

_______________ m²
Answer:
0.05 m²

Explanation:
Given,
Diameter = 0.24 m, π = 3.14
Radius = d/2
r = 0.24/2
r = 0.12 m
A = π × r²
A = 3.14 x 0.12 x 0.12
A = 0.0452 or 0.05 sq. m.