﻿ Area of a Circle Worksheet | Problems & Solutions Area of a Circle Worksheet

Area of a Circle Worksheet
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1.
What is the area of a circular field with a radius of 1.3 yd?
[Use $\pi$ = 3.14.] a. 3.31 yd2 b. 7.31 yd2 c. 8.71 yd2 d. 5.31 yd2

Solution:

The area of a circle = π r2

= π × (1.3)2

= 3.14 × 1.69
[Substitute π = 3.14.]

= 5.31 yd2

2.
What is the area of the circle with a circumference of 24 ft? [Use $\pi$ = 3.14] a. 60.82 ft2 b. 53.82 ft2 c. 50.82 ft2 d. 45.82 ft2

Solution:

Circumference of the circle = 24 ft

Circumference of the circle, 2 x π x r = 2 x 3.14 x r = 24

r = 242x3.14
[Divide each side by (2 x 3.14)]

= 3.82 ft

Area of the circle = πr2 = 3.14 x 3.82 x 3.82
[Substitute r = 3.82]

= 45.82 ft2

The area of the circle is 45.82 ft2

3.
A circular park of radius 31 m has a path of width 4 m along the inner circumference. What is the area of the path?  a. 961π m2 b. 729π m2 c. 232π m2 d. 237π m2

Solution:

Radius of the outer circle = 31 m

Area of the outer circle = πr2

= π x 312
[Substitute r = 31.]

= 961π m2
[Multiply.]

Radius of the inner circle = 31 - 4 = 27 m

Area of the inner circle = πr2

= π x 272
[Substitute r = 27.]

= 729π m2
[Multiply.]

Area of the path = Area of the outer circle - Area of the inner circle

= 961π - 729π
[Substitute the values.]

= 232π
[Subtract.]

Area of the path is 232π m2.

4.
The diameter of a small pizza is 10 inches. What is its area? [Use $\pi$ = 3.14.] a. 78.5 in.2 b. 80.5 in.2 c. 82.5 in.2 d. 76.5 in.2

Solution:

The radius of the pizza = Diameter / 2 = 10 / 2
[Substitute d = 10.]

= 5 inches

Area of a circle = πr2.

= π × 52
[Substitute the values.]

= 3.14 × 25
[Substitute π = 3.14.]

= 78.5 in.2

5.
The circumference of a circular swimming pool at its bottom is 83 ft. What is the area of the bottom of the pool?[Use $\pi$ = 3.14.] a. About 548.77 ft b. About 548.77 ft2 c. About 548.77 ft3 d. About 528.77 ft3

Solution:

Circumference of a circle = 2πr

2 × 3.14 × r = 83
[Substitute π = 3.14.]

r = 832 × 3.14
[Divide each side by (2 × 3.14).]

= 13.22 ft

Area of the bottom = πr2

= 3.14 × 13.22 × 13.22
[Substitute r = 13.22.]

548.77 ft2
[Simplify.]

The area of the bottom is about 548.77 ft2.

6.
What is the radius of the circle?  a. √3 ft. b. 3√2 ft. c. 2√5 ft. d. 3√3 ft.

Solution:

From the figure, ABCD is a square of side 6 ft and OD is the radius of the circle.

The length of the diagonal, BD = 2 x radius = 2r
[Formula.]

From the figure, AB2 + AD2 = BD2
[Since ABD forms a right triangle.]

62 + 62 = (2r)2
[Substitue the values.]

36 + 36 = 4r2

72 = 4r2

18 = r2
[Divide each side by 4.]

3√2 = r
[Take square root on both sides.]

So, radius of the circle, r = 3√2 ft.

7.
What is the area of the colored region in the figure?
[Use $\pi$ = 3.14.]  a. 122.62 cm2 b. 54 cm2 c. 176.62 cm2 d. 117.62 cm2

Solution:

From the figure, the base and height of the right triangle are 12 cm and 9 cm respectively.

In a right triangle, Hypotenuse2 = Base2 + Height2.

AC2 = AB2 + BC2

AC2 = 122 + 92

AC2 = 144 + 81 = 225

AC = √225

AC = 15
[ √225 = 15 ]

AC is the diameter of the circle.
So, radius of the circle = AC / 2 = 15 / 2 = 7.5.

Area of the colored region = Area of the circle - Area of the triangle.

= 3.14 x 7.5 x 7.5
Area of the circle = πr2
[Substitute r = 7.5 and π = 3.14.]

= 176.62 cm2

Area of the triangle = 1 / 2 x base x height

= 12 x 12 x 9
[Substitute base = 12 and height = 9.]

= 54 cm2

The area of the colored region = 176.62 - 54 = 122.62 cm2.

8.
What is the area of the colored region in the figure?
[Use $\pi$ = 3.14.]  a. 100 cm2 b. 78.5 cm2 c. 21.5 cm2 d. None of the above

Solution:

From the figure, the side of the square is 10 cm and the radius of the circle is 5 cm.

Area of the colored region = Area of the square - Area of the circle.

Area of the square = a2 = 10 x 10
[Substitute a = 10.]

= 100 cm2

= 3.14 x 5 x 5
Area of the circle = πr2
[Substitute r = 5 and π = 3.14.]

= 78.5 cm2

The area of the colored region = 100 - 78.5 = 21.5 cm2.

9.
A goat is tethered to a stake with a 5 m rope. The goat can graze to the full length of the rope and 360° around the stake. What is the area of the circle in which the goat can graze?
[Use $\pi$ = 3.14.] a. 78.50 m2 b. 83.50 m2 c. 80.50 m2 d. 73.50 m2

Solution:

Area of the circular region where the goat can graze = πr2

= 3.14 × 5 × 5
[Substitute r = 5 and π = 3.14.]

= 78.50 m2

The area of the circle the goat can graze is 78.50 m2.

10.
A circular cake is cut into equal pieces in such a way that each piece makes an angle of 45o at the center. Find the number of pieces that are cut. a. 10 b. 6 c. 12 d. 8

Solution:

The complete angle at the center of a circle is 360o.

= 360o/45o
=8
Number of pieces = complete angle / angle subtended by each piece at the center.
[Substitute the values.]

So, the total number of pieces that are cut from the cake is 8.