Volume of Pyramids and Cones Worksheet

**Page 6**

51.

What is the base area of a rectangular pyramid, whose height is 12 cm and volume is 120 cm^{3}?

a. | 20 cm ^{2} | ||

b. | 10 cm ^{2} | ||

c. | 60 cm ^{2} | ||

d. | 30 cm ^{2} |

[Volume formula.]

The base area of the rectangular pyramid =

=

[Substitute the values.]

=

[Multiply 3 by 120.]

= 30

[Divide.]

The base area of the rectangular pyramid is 30 cm

Correct answer : (4)

52.

What is the base width of a rectangular pyramid, if its length, height and volume are 5 cm, 3 cm and 45 cm^{3} respectively?

a. | 9 cm | ||

b. | 3 cm | ||

c. | 4 cm | ||

d. | 14 cm |

[Volume formula.]

The base width of the rectangular pyramid =

=

[Substitute the values.]

=

[Simplify.]

= 9

[Divide the numerator and the denominator by 15.]

So, base width of the rectangular pyramid is 9 cm.

Correct answer : (1)

53.

What is the base area and volume of the rectangular pyramid, whose length, width, and height are 13.8 cm, 9.2 cm and 11.5 cm respectively?

a. | 136.96 cm ^{2} and 496.68cm^{3} | ||

b. | 146.96 cm ^{2} and 506.68cm^{3} | ||

c. | 126.96 cm ^{2} and 1460.04 cm^{3} | ||

d. | 126.96 cm ^{2} and 486.68 cm^{3} |

= 13.8 × 9.2

[Substitute the values.]

= 126.96 cm

[Multiply 13.8 by 9.2.]

The volume of a rectangular pyramid = (

= (

[Substitute the values.]

=

[Multiply 126.96 by 11.5.]

= 486.68 cm

[Divide.]

The base area and volume of the rectangular pyramid are 126.96 cm

Correct answer : (4)

54.

Find the volume of the figure shown, if $A$$B$ = 6 ft and $C$$O$ = $C$′$O$ = 15 ft.

a. | 88$\pi $ ft ^{3} | ||

b. | 90$\pi $ ft ^{3} | ||

c. | 43$\pi $ ft ^{3} | ||

d. | 45$\pi $ ft ^{3} |

and the height of each cone,

=

The base radius of the cone,

[Substitute diameter = 6 ft.]

= 3 ft

Volume of each cone,

[Formula.]

=

[Substitute

= 45

[Simplify.]

The volume of the figure = 2 ×

[Since the figure contains two identical cones.]

= 2 × 45

[Substitute,

= 90

The volume of the figure is 90

Correct answer : (2)

55.

Find the volume of the rectangular pyramid, if $a$ = 7 in., $b$ = 6 in., $c$ = 8 in..

a. | 212 in. ^{3} | ||

b. | 336 in. ^{3} | ||

c. | 112 in. ^{3} | ||

d. | 132 in. ^{3} |

Volume of a rectangular pyramid = (

=

[Substitute the values.]

=

= 112 in.

[Simplify.]

The volume of the rectangular pyramid is 112 in.

Correct answer : (3)

56.

Find the volume of the rectangular pyramid, whose base length($a$), diagonal of the base($b$), and height($h$) of the pyramid are 8.8 in., 11 in., and 13.2 in. respectively.

a. | 255.55 in. ^{3} | ||

b. | 285.55 in. ^{3} | ||

c. | 766.65 in. ^{3} | ||

d. | 275.55 in. ^{3} |

According to the right triangle property, 8.8

77.44 +

[Subtract 77.44 from 121.]

So, width of the rectangular base = 6.6 in.

Volume of the rectangular pyramid = (

= (

[Substitute the values.]

=

[Multiply 8.8, 6.6, and 13.2.]

= 255.55 in.

[Divide.]

Volume of the rectangular pyramid is 255.55 in.

Correct answer : (1)

57.

What is the volume of the figure shown?[Given $r$ = 6.6 cm, $h$ = 11 cm.]

a. | 319.4$\pi $ cm ^{3} | ||

b. | 349.4$\pi $ cm ^{3} | ||

c. | 369.4$\pi $ cm ^{3} | ||

d. | 299.4$\pi $ cm ^{3} |

and the height of each cone,

Volume of each cone,

[Volume formula.]

=

[Substitute

= 159.7

[Simplify.]

The volume of the figure = 2 ×

[The figure contains two identical cones.]

= 2 × 159.7

[Substitute

= 319.4

The volume of the figure is 319.4

Correct answer : (1)

58.

What is the volume of the figure?

[Given $l$ = 11 cm, $h$ = 6.6 cm, $w$ = 8.8 cm.]

a. | 212.96 cm ^{3} | ||

b. | 1277.76 cm ^{3} | ||

c. | 425.92 cm ^{3} | ||

d. | 638.88 cm ^{3} |

The base area of the rectangular pyramid = length × width

= 11 × 8.8

[Substitute the values.]

= 96.8 cm

[Multiply.]

The volume of the rectangular pyramid = (

= (

[Substitute the values.]

= 212.96 cm

[Simplify.]

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

= 2 × 212.96

[Substitute volume = 212.96]

= 425.92 cm

[Multiply.]

The volume of the figure is 425.92 cm

Correct answer : (3)

59.

Find the volume of the cone in the figure.

[Given $r$ = 3.6 in., $h$ = 5.4 in..]

a. | 15.55π in. ^{3} | ||

b. | 34.99π in. ^{3} | ||

c. | 23.33π in. ^{3} | ||

d. | 33.33π in. ^{3} |

Volume of the cone =

[Formula.]

=

[Substitute base radius,

=

[Divide numerator and denominator by 3.]

= 23.33

[Simplify.]

The volume of the cone is 23.33π in.

Correct answer : (3)

60.

What is the volume of the cone whose diameter($d$) is 7.2 cm and slant height($l$) is 6 cm?

a. | 20.7 cm ^{3} | ||

b. | 41.4π cm ^{3} | ||

c. | 30.7π cm ^{3} | ||

d. | 20.7π cm ^{3} |

[Since, the diameter of the cone is 7.2 cm.]

From the figure,

[Pythagorean theorem.]

[Substitute

12.9 +

[Evaluate powers.]

[Subtract 12.9 from both sides.]

[Take square root on both sides.]

The height of the cone is 4.8 cm.

The volume of the cone =

[Volume formula.]

=

[Substitute

= 20.7π cm

[Simplify the expression.]

The volume of the cone is 20.7π cm

Correct answer : (4)