Area and Circumference of a Circle Worksheet

**Page 1**

1.

The diameter of a circular garden is 32 m. What is the new circumference of the garden, if its radius is decreased by 6 m? [ Use $\pi $ = 3.14]

a. | 66.80 m | ||

b. | 125.60 m | ||

c. | 64.80 m | ||

d. | 62.80 m |

So, the radius of the circular garden =

If the radius is decreased by 6 m, then the new radius = 16 - 6 = 10 m.

The new circumference of the garden = 2 ×

[Formula.]

= 2 × 3.14 × 10

[Substitute the values.]

= 62.80 m.

[Multiply.]

So, the new circumference of the garden = 62.80 m.

Correct answer : (4)

2.

A circular park of radius 300 yd has a circular pavement around it. What is the area of the pavement, if the width of the pavement is 4 yd? [Use $\pi $ = 3.14]

a. | 2426$\pi $ yd ^{2} | ||

b. | 7248 yd ^{2} | ||

c. | 2416$\pi $ yd ^{2} | ||

d. | None of the above |

[Formula.]

Area of the circular park with radius 300 yd =

Area of the park along with the pavement =

Area of the pavement = area of the park along with the pavement - area of the park.

Area of the pavement =

=

[(a

=

[Simplify.]

= 2416

So, the area of the pavement is 2416

Correct answer : (3)

3.

What is the area of the shaded region in the figure?[Use $\pi $ = 3.14]

a. | 177.7 cm ^{2} | ||

b. | 172.7 cm ^{2} | ||

c. | 127.7 cm ^{2} | ||

d. | None of the above |

Area of the bigger circle =

[Formula.]

= 3.14 x 8

[Substitute the value of the radius.]

= 3.14 x 8 x 8

[Expand 8

= 200.96 cm

[Multiply.]

Area of the bigger circle = 200.96 cm

Area of the smaller circle =

[Formula.]

= 3.14 x 3

[Substitute the radius of the smaller circle.]

= 3.14 x 3 x 3

[Expand 3

= 28.26 cm

[Multiply.]

Area of the smaller circle = 28.26 cm

Area of the shaded region = area of the bigger circle Ã¢â‚¬â€œ area of the smaller circle.

= 200.96 - 28.26

[Substitute the values.]

= 172.7

[Subtract.]

So, area of the shaded region is 172.7 cm

Correct answer : (2)

4.

The radius of a sector of a circle is 2 cm and its central angle is 90 degrees. Calculate the perimeter of the sector.

a. | 4 cm | ||

b. | $\pi $ cm | ||

c. | (4 + $\pi $) cm | ||

d. | (2 + $\pi $) cm |

[Formula.]

= 2

[Arc length of a circle =

Perimeter of a sector = 2 × 2 +

[Substitute the value of

= 4 +

[Simplify]

So, perimeter of the sector is (4 +

Correct answer : (3)

5.

Find the area of the sector AOB.

a. | 3.25$\pi $ cm ^{2} | ||

b. | 3$\pi $ cm ^{2} | ||

c. | 6.75$\pi $ cm ^{2} | ||

d. | 4.5 cm ^{2} |

[Formula.]

[Convert degrees to radians.]

=

[Substitute the values.]

= 6.75

[Simplify.]

So, the area of the sector of the circle is 6.75

Correct answer : (3)

6.

Find the area of the sector POQ of the circle of radius 8 cm.

a. | 8 cm ^{2} | ||

b. | 4 cm ^{2} | ||

c. | 8$\pi $ cm ^{2} | ||

d. | 4$\pi $ cm ^{2} |

[Formula.]

45° = 45 ×

[Convert degrees to radians.]

=

[Substitute the values.]

= 8

[Simplify.]

So, the area of the sector of the circle is 8

Correct answer : (3)

7.

The central angle of a sector is 30° and the radius of the circle is 6 cm. Find the area of the sector of the circle.

a. | $\frac{3\pi}{2}$ square cm | ||

b. | $\frac{2\pi}{3}$ square cm | ||

c. | 3$\pi $ square cm | ||

d. | 6$\pi $ square cm |

[Formula.]

30° = 30 ×

[Convert degrees to radians.]

=

[Substitute the values.]

= 3

[Simplify.]

So, the area of the sector of the circle is 3

Correct answer : (3)

8.

The angle of a sector is 90 degrees and the radius of the circle is 3 cm. Calculate the area of the sector.

a. | $\frac{3\pi}{2}$ square cm | ||

b. | $\frac{9\pi}{2}$ square cm | ||

c. | $\frac{9\pi}{4}$ square cm | ||

d. | $\frac{3\pi}{4}$ square cm |

[Formula.]

90° = 90 ×

[Convert degrees to radians.]

=

[Substitute the values.]

=

So, the area of the sector of the circle is

Correct answer : (3)

9.

If the diameter of a circle is doubled, how is the circumference changed?

a. | multiplied by 2 | ||

b. | divided by 2 | ||

c. | divided by 4 | ||

d. | multiplied by 4 |

If diameter of a circle is

If the diameter of the circle is doubled, then diameter of the new circle will be 2

Circumference of the new circle = π(2

Therefore, circumference of the new circle will be two times the original circumference of the circle.

Correct answer : (1)

10.

If the radius of a circle is multiplied by 2, how is the area changed?

a. | multiplied by 4 | ||

b. | divided by 4 | ||

c. | divided by 2 | ||

d. | multiplied by 2 |

If the radius of a circle is

If the radius of the circle is multiplied by 2, then radius of the new circle will be 2

Area of the new circle = π(2

Therefore, area of the new circle will be four times the original area of the circle.

Correct answer : (1)