Area of a Circle Worksheet

**Page 1**

1.

What is the area of a circular field with a radius of 1.3 yd?

[Use $\pi $ = 3.14.]

a. | 3.31 yd ^{2} | ||

b. | 7.31 yd ^{2} | ||

c. | 8.71 yd ^{2} | ||

d. | 5.31 yd ^{2} |

=

= 3.14 × 1.69

[Substitute

= 5.31 yd

Correct answer : (4)

2.

What is the area of the circle with a circumference of 24 ft? [Use $\pi $ = 3.14]

a. | 60.82 ft ^{2} | ||

b. | 53.82 ft ^{2} | ||

c. | 50.82 ft ^{2} | ||

d. | 45.82 ft ^{2} |

Circumference of the circle, 2 x

[Divide each side by (2 x 3.14)]

= 3.82 ft

Area of the circle =

[Substitute

= 45.82 ft

The area of the circle is 45.82 ft

Correct answer : (4)

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 m ^{2} | ||

b. | 729π m ^{2} | ||

c. | 232π m ^{2} | ||

d. | 237π m ^{2} |

Area of the outer circle =

=

[Substitute

= 961

[Multiply.]

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

Area of the inner circle =

=

[Substitute

= 729

[Multiply.]

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

= 961

[Substitute the values.]

= 232

[Subtract.]

Area of the path is 232

Correct answer : (3)

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} |

[Substitute

= 5 inches

Area of a circle =

=

[Substitute the values.]

= 3.14 × 25

[Substitute

= 78.5 in.

Correct answer : (1)

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 ft ^{2} | ||

c. | About 548.77 ft ^{3} | ||

d. | About 528.77 ft ^{3} |

2 × 3.14 ×

[Substitute

[Divide each side by (2 × 3.14).]

= 13.22 ft

Area of the bottom =

= 3.14 × 13.22 × 13.22

[Substitute

[Simplify.]

The area of the bottom is about 548.77 ft

Correct answer : (2)

6.

What is the radius of the circle?

a. | √3 ft. | ||

b. | 3√2 ft. | ||

c. | 2√5 ft. | ||

d. | 3√3 ft. |

The length of the diagonal, BD = 2 x radius = 2

[Formula.]

From the figure, AB

[Since ABD forms a right triangle.]

6

[Substitue the values.]

36 + 36 = 4

72 = 4

18 =

[Divide each side by 4.]

3√2 =

[Take square root on both sides.]

So, radius of the circle,

Correct answer : (2)

7.

What is the area of the colored region in the figure?

[Use $\pi $ = 3.14.]

a. | 122.62 cm ^{2} | ||

b. | 54 cm ^{2} | ||

c. | 176.62 cm ^{2} | ||

d. | 117.62 cm ^{2} |

In a right triangle, Hypotenuse

AC

AC

AC

AC = √225

AC = 15

[ √225 = 15 ]

AC is the diameter of the circle.

So, radius of the circle =

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 =

[Substitute

= 176.62 cm

Area of the triangle =

=

[Substitute base = 12 and height = 9.]

= 54 cm

The area of the colored region = 176.62 - 54 = 122.62 cm

Correct answer : (1)

8.

What is the area of the colored region in the figure?

[Use $\pi $ = 3.14.]

a. | 100 cm ^{2} | ||

b. | 78.5 cm ^{2} | ||

c. | 21.5 cm ^{2} | ||

d. | None of the above |

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

Area of the square =

[Substitute

= 100 cm

= 3.14 x 5 x 5

Area of the circle =

[Substitute

= 78.5 cm

The area of the colored region = 100 - 78.5 = 21.5 cm

Correct answer : (3)

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 m ^{2} | ||

b. | 83.50 m ^{2} | ||

c. | 80.50 m ^{2} | ||

d. | 73.50 m ^{2} |

= 3.14 × 5 × 5

[Substitute

= 78.50 m

The area of the circle the goat can graze is 78.50 m

Correct answer : (1)

10.

A circular cake is cut into equal pieces in such a way that each piece makes an angle of 45^{o} at the center. Find the number of pieces that are cut.

a. | 10 | ||

b. | 6 | ||

c. | 12 | ||

d. | 8 |

= 360

=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.

Correct answer : (4)