﻿ Volume of Pyramids and Cones Worksheet - Page 6 | Problems & Solutions
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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 cm3? a. 20 cm2 b. 10 cm2 c. 60 cm2 d. 30 cm2

#### Solution:

The volume of the rectangular pyramid = (1 / 3) × base area × height
[Volume formula.]

The base area of the rectangular pyramid = 3 × volumeheight

= 3 × 12012
[Substitute the values.]

= 36012
[Multiply 3 by 120.]

= 30
[Divide.]

The base area of the rectangular pyramid is 30 cm2.

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 cm3 respectively? a. 9 cm b. 3 cm c. 4 cm d. 14 cm

#### Solution:

Volume of the rectangular pyramid = (1 / 3) × length × width × height
[Volume formula.]

The base width of the rectangular pyramid = 3 × volumelength × height

= 3 × 455 × 3
[Substitute the values.]

= 13515
[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 cm2 and 496.68cm3 b. 146.96 cm2 and 506.68cm3 c. 126.96 cm2 and 1460.04 cm3 d. 126.96 cm2 and 486.68 cm3

#### Solution:

The base area of the rectangular pyramid = length × width

= 13.8 × 9.2
[Substitute the values.]

= 126.96 cm2
[Multiply 13.8 by 9.2.]

The volume of a rectangular pyramid = (1 / 3) × base area × height

= (13) × 126.96 × 11.5
[Substitute the values.]

= 1460.043
[Multiply 126.96 by 11.5.]

= 486.68 cm3
[Divide.]

The base area and volume of the rectangular pyramid are 126.96 cm2 and 486.68 cm3.

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$\pi$ ft3 b. 90$\pi$ ft3 c. 43$\pi$ ft3 d. 45$\pi$ ft3

#### Solution:

From the figure, the base diameter of each cone, d = AB = 6 ft
and the height of each cone, h = CO = 15 ft.

= 62
The base radius of the cone, r = diameter2
[Substitute diameter = 6 ft.]

= 3 ft

Volume of each cone, V = 1 / 3πr2h
[Formula.]

= 13 × π × 32 × 15
[Substitute r = 3 and h = 15.]

= 45π ft3
[Simplify.]

The volume of the figure = 2 × V
[Since the figure contains two identical cones.]

= 2 × 45π ft3
[Substitute, V = 45π ft3.]

= 90π ft3

The volume of the figure is 90π ft3.

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

#### Solution:

From the figure, the length, width, and height of the rectangular pyramid are 7 in., 6 in., and 8 in. respectively.

Volume of a rectangular pyramid = (1 / 3) × length × width × height

= 13 × 7 × 6 × 8
[Substitute the values.]

= 3363 in.3

= 112 in.3
[Simplify.]

The volume of the rectangular pyramid is 112 in.3.

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

#### Solution:

The rectangular base consists of two right triangles.

According to the right triangle property, 8.82 + w2 = 112, where w is the width of the rectangular base.

77.44 + w2 = 121

w2 = 121 - 77.44

w2 = 43.56
[Subtract 77.44 from 121.]

w = 43.56

w = 6.6 in.

So, width of the rectangular base = 6.6 in.

Volume of the rectangular pyramid = (1 / 3) × length × width × height

= (1 / 3) × 8.8 × 6.6 × 13.2
[Substitute the values.]

= 766.65 / 3
[Multiply 8.8, 6.6, and 13.2.]

= 255.55 in.3
[Divide.]

Volume of the rectangular pyramid is 255.55 in.3

Correct answer : (1)
57.
What is the volume of the figure shown?[Given $r$ = 6.6 cm, $h$ = 11 cm.]  a. 319.4$\pi$ cm3 b. 349.4$\pi$ cm3 c. 369.4$\pi$ cm3 d. 299.4$\pi$ cm 3

#### Solution:

From the figure, the base radius of each cone, r = 6.6 cm
and the height of each cone, h = 11 cm

Volume of each cone, V = 1 / 3πr2h
[Volume formula.]

= 1 / 3 × π × (6.6)2 × 11
[Substitute r = 6.6 and h = 11.]

= 159.7π cm3
[Simplify.]

The volume of the figure = 2 × V
[The figure contains two identical cones.]

= 2 × 159.7π
[Substitute V = 159.7π.]

= 319.4π cm3

The volume of the figure is 319.4π cm3.

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 cm3 b. 1277.76 cm3 c. 425.92 cm3 d. 638.88 cm3

#### Solution:

From the figure, the length, width and height of the rectangular pyramid are 11 cm, 8.8 cm, and 6.6 cm.

The base area of the rectangular pyramid = length × width

= 11 × 8.8
[Substitute the values.]

= 96.8 cm2
[Multiply.]

The volume of the rectangular pyramid = (1 / 3) × base area × height

= (1 / 3) × 96.8 × 6.6
[Substitute the values.]

= 212.96 cm3
[Simplify.]

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

= 2 × 212.96
[Substitute volume = 212.96]

= 425.92 cm3
[Multiply.]

The volume of the figure is 425.92 cm3.

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

#### Solution:

From the figure, base radius of the cone, r = 3.6 in. and height, h = 5.4 in.

Volume of the cone = 1 / 3πr2h
[Formula.]

= 1 / 3 × π × 3.62 × 5.4
[Substitute base radius, r = 3.6 in. and height, h = 5.4 in..]

= 69.98π3
[Divide numerator and denominator by 3.]

= 23.33π
[Simplify.]

The volume of the cone is 23.33π in.3.

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 cm3 b. 41.4π cm3 c. 30.7π cm3 d. 20.7π cm3

#### Solution:

The base radius of the cone, r = diameter2 = 7.2 / 2 = 3.6 cm
[Since, the diameter of the cone is 7.2 cm.]

From the figure, AB2 + BC2 = AC2
[Pythagorean theorem.]

h2 + (3.6)2 = (6)2
[Substitute AB = h, BC = 3.6 cm, and AC = 6 cm.]

12.9 + h2 = 36
[Evaluate powers.]

h2 = 36 - 12.9
[Subtract 12.9 from both sides.]

h2 = 23.1

h = 23.1 = 4.8
[Take square root on both sides.]

The height of the cone is 4.8 cm.

The volume of the cone = 1 / 3πr2h
[Volume formula.]

= 1 / 3 × π × (3.6)2 × 4.8
[Substitute r = 3.6 and h = 4.8.]

= 20.7π cm3
[Simplify the expression.]

The volume of the cone is 20.7π cm3.

Correct answer : (4)

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