Volume of Pyramids and Cones Worksheet

**Page 7**

61.

The radius of the base of a right circular cone is 3$r$ mm and its height is equal to the radius of the base. Find its volume in mm^{3}.

a. | 14π$r$ ^{3} mm^{3} | ||

b. | 9π$r$ ^{3} mm^{3} | ||

c. | 4π$r$ ^{3}mm^{3} | ||

d. | 11π$r$ ^{3}mm^{3} |

Volume of a cone =

[Formula.]

=

[Substitute the values.]

= 9

[Simplify.]

The volume of the right circular cone = 9

Correct answer : (2)

62.

A tent is in the shape of a cylinder with a conical top. The radius of the base of the tent is 9 m. The height of the cylindrical part is 16 m and that of the conical part is 25 m. Find the volume of air that occupies the tent. (Round the answer to one decimal place.)

a. | 6173.9 m ^{3} | ||

b. | 3600 m ^{3} | ||

c. | 6188.9 m ^{3} | ||

d. | 50 m ^{3} |

[Formula.]

= 3.14 × 9

[Substitute the values.]

= 4069.44

[Simplify.]

Volume of the cylindrical part = 4069.44 m

Volume of Conical part =

[Formula.]

=

[Substitute the values.]

= 2119.50

[Simplify.]

Volume of the cone = 2119.50 m

= (2119.50 + 4069.44) m

Volume of air that occupies the tent = volume of cylindrical part + volume of conical part

[Round the answer to one decimal place.]

Volume of air that occupies the tent = 6188.9 m

Correct answer : (3)

63.

Find the volume of the square pyramid, if $s$ = 9 in., $h$ = 6 in..

a. | 162 in. | ||

b. | 15 in. ^{2} | ||

c. | 54 in. ^{3} | ||

d. | 162 in. ^{3} |

[Volume formula.]

Base area of the square pyramid = (base edge)

[The base is a square.]

= 9

= 81 in.

[Multiply.]

Volume of the square pyramid =

[Substitute base area = 81 and height = 6.]

= 162 in.

[Simplify.]

So, the volume of the square pyramid is 162 in.

Correct answer : (4)

64.

Find the height of the cone whose volume is 480$\pi $ cm^{3} and base radius is 12 cm.

a. | 10 cm | ||

b. | 13 cm | ||

c. | 30 cm | ||

d. | 20 cm |

Volume of the cone,

[Volume formula.]

The height of the cone,

=

[Substitute

= 10 cm

[Simplify.]

The height of the cone is 10 cm.

Correct answer : (1)

65.

What is the base radius of a cone, whose volume is 48π ft^{3} and height is 4 ft?

a. | 9 ft | ||

b. | 8 ft | ||

c. | 5 ft | ||

d. | 6 ft |

Volume of the cone, V = (

[Formula.]

[Rewrite the formula.]

=

[Substitute V = 48π and

= 6 ft

[Simplify.]

The base radius of the cone is 6 ft.

Correct answer : (4)

66.

What is the volume of the cone whose diameter is 12 ft and slant height is 10 ft?

a. | 51π ft ^{3} | ||

b. | 288π ft ^{3} | ||

c. | 36π ft ^{3} | ||

d. | 96π ft ^{3} |

The base radius of the cone,

[Since the diameter of the cone is 12 ft.]

From the figure, AB

[Pythagorean theorem.]

[Substitute AB =

[Evaluate powers.]

[Subtract 36 from both sides.]

[Subtract.]

[Take square root on both sides.]

The height of the cone is 8 ft.

The volume of the cone =

[Volume formula.]

=

[Substitute

= 96π ft

[Simplify the expression.]

The volume of the cone is 96π ft

Correct answer : (4)

67.

Base radius of a cone is 5 in. and its height is 15 in. If the height and the radius of the cone are doubled, then find the volume of the new cone.

a. | 3140 in. ^{3} | ||

b. | 9420 in. ^{3} | ||

c. | 1570 in. ^{3} | ||

d. | 1046 in. ^{3} |

[Since base radius of new cone is double the radius of initial cone.]

Height of the new cone = 2 × height of the initial cone = 2 × 15 = 30 in.

[Since height of new cone is double the height of initial cone.]

Volume of cone =

[Formula.]

= 3140

Volume of new cone =

[Substitute the values in the formula and simplify.]

Volume of the new cone is 3140 in.

Correct answer : (1)

68.

What is the volume of a cone, if its radius is 9 cm and its curved surface area is 423.9 cm^{2}? (Round the answer to the nearest whole number.)

a. | 1022 cm ^{3} | ||

b. | 1014 cm ^{3} | ||

c. | 1025 cm ^{3} | ||

d. | 1017 cm ^{3} |

[Formula.]

π

[Since curved surface area of cone is 423.9 cm

3.14 × 9 ×

[Substitute the values of

[Simplify.]

Slant height of the cone (

Height of cone

Height of cone

[Substitute the values.]

Height of the cone = 12 cm

[Take the square root of each side.]

Volume of cone =

[Formula.]

=

[Substitute the values.]

= 1017.36

[Simplify.]

[Round the answer to the nearest whole number.]

Volume of the cone = 1017 cm

Correct answer : (4)