Volume of Pyramids and Cones Worksheet

**Page 4**

31.

What is the volume of the figure shown?

a. | 25$\pi $ in ^{3} | ||

b. | 40$\pi $ in ^{3} | ||

c. | 30$\pi $ in ^{3} | ||

d. | 26$\pi $ in ^{3} |

and the height of each cone,

Volume of each cone, V =

[Volume formula.]

=

[Substitute

= 15

[Simplify.]

The volume of the figure = 2 x V

[The figure contains two identical cones.]

= 2 × 15

[Substitute V = 15

= 30

The volume of the figure is 30

Correct answer : (3)

32.

Find the volume of the figure.

a. | 60 in. ^{3} | ||

b. | 40 in. ^{3} | ||

c. | 120 in. ^{3} | ||

d. | 20 in. ^{3} |

The base area of the rectangular pyramid = length × width

= 5 × 4

[Substitute the values.]

= 20 in.

[Multiply.]

The volume of the rectangular pyramid = (

= (

[Substitute the values.]

= 20 in.

[Simplify.]

The volume of the figure = 2 × volume of the rectangular pyramid

= 2 × 20

[Substitute volume = 20.]

= 40 in.

[Multiply.]

The volume of the figure is 40 in.

Correct answer : (2)

33.

Find the volume of the cone in the figure.

a. | 11π cm ^{3} | ||

b. | 14π cm ^{3} | ||

c. | 13π cm ^{3} | ||

d. | 15π cm ^{3} |

Volume of the cone =

[Formula.]

=

[Substitute base radius,

=

[Divide numerator and denominator by 3.]

= 15π

[Simplify.]

The volume of the cone is 15π cm.

Correct answer : (4)

34.

What is the volume of the cone whose diameter is 6 ft and slant height is 5 ft?

a. | 13 ft ^{3} | ||

b. | 11 ft ^{3} | ||

c. | 14 ft ^{3} | ||

d. | 12π ft ^{3} |

[Since the diameter of the cone is 6 ft.]

From the figure, AB

[Pythagorean theorem.]

[Substitute AB =

9 +

[Evaluate powers.]

[Subtract 9 from both sides.]

[Subtract 9.]

[Take square root on both sides.]

The height of the cone is 4 ft.

The volume of the cone =

[Volume formula.]

=

[Substitute

= 12

[Simplify the expression.]

The volume of the cone is 12π ft

Correct answer : (4)

35.

What is the volume of the cone whose diameter is 6 ft and slant height is 5 ft?

a. | 11π ft ^{3} | ||

b. | 14π ft ^{3} | ||

c. | 13π ft ^{3} | ||

d. | 12π ft ^{3} |

= 3 ft

The base radius of the cone,

[Since the diameter of the cone is 6 ft.]

From the figure, AB

[Pythagorean theorem.]

[Substitute AB =

[Evaluate powers.]

[Subtract 9 from both sides.]

[Subtract.]

[Take square root on both sides.]

The height of the cone is 4 ft.

The volume of the cone =

[Volume formula.]

=

[Substitute

= 12π ft

[Simplify the expression.]

The volume of the cone is 12π ft

Correct answer : (4)

36.

If the radius of the base of a right circular cone is 6$r$ mm. and its height is equal to the radius of the base, find its volume in mm.^{3}.

a. | 67π$r$ ^{3} | ||

b. | 74π$r$ ^{3} | ||

c. | 72π$r$ ^{3} | ||

d. | 77π$r$ ^{3} |

Volume of a cone =

[Formula.]

=

[Substitute the values.]

= 72

[Simplify.]

The volume of the right circular cone = 72

Correct answer : (3)

37.

What is the volume of a cone, if its radius is 3 cm and its curved surface area is 47.1 cm^{2}? (Round the answer to the nearest whole number.)

a. | 113 cm ^{3} | ||

b. | 141 cm ^{3} | ||

c. | 38 cm ^{3} | ||

d. | 47 cm ^{3} |

[Formula.]

[Since curved surface area of cone is 47.1 cm

3.14 x 3 x

[Substitute the values of π and

[Simplify.]

Slant height of the cone(

(Height of cone)

(Height of cone)

[Substitute the values.]

Height of cone = 4 cm

[Take the square root of each side.]

Volume of cone =

[Formula.]

=

[Substitute the values.]

= 37.68

[Simplify.]

[Round the answer to the nearest whole number.]

Volume of the cone = 38 cm

Correct answer : (3)

38.

The base of a pyramid is a right triangle and two sides containing the right angle are 4 ft and 4 ft. If height of the pyramid is 15 ft, then find the volume of the pyramid.

a. | 35 ft ^{3} | ||

b. | 40 ft ^{3} | ||

c. | 49 ft ^{3} | ||

d. | 46 ft ^{3} |

Base area of the pyramid = area of right triangle =

Volume of the pyramid =

[Formula.]

=

[Substitute the values.]

= 40

[Simplify.]

Volume of the pyramid = 40 ft

Correct answer : (2)

39.

The height of a right circular cone is 12 cm. If its volume is 1024π cm.^{3}, what is the slant height of the cone?

a. | 20 cm | ||

b. | 29 cm | ||

c. | 25 cm | ||

d. | 16 cm |

[Formula.]

1024π =

[Substitute the values.]

[Simplify.]

Slant height of cone (l) = √(

= √ (256 + 12

[Substitute the values.]

= √ (400) = 20

[Simplify.]

Slant height of the cone = 20 cm.

Correct answer : (1)

40.

State whether the statement is true or false. "The volume of a cone is equal to one third the volume of a cylinder with the same base radius and the same height."

a. | True | ||

b. | False |

Volume of cylinder = π

[Formula.]

Volume of cone =

[Formula.]

=

=

[Since volume of cylinder is π

Volume of cone =

So, the statement is true.

Correct answer : (1)