﻿ Volume of Pyramids and Cones Worksheet - Page 7 | Problems & Solutions
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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 mm3. a. 14π$r$3 mm3 b. 9π$r$3 mm3 c. 4π$r$3mm3 d. 11π$r$3mm3

#### Solution:

Height of a cone = base radius of the cone = 3r mm.

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

= 13 × π × (3r)2 × 3r
[Substitute the values.]

= 9πr3
[Simplify.]

The volume of the right circular cone = 9πr3 mm3.

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 m3 b. 3600 m3 c. 6188.9 m3 d. 50 m3

#### Solution:

Volume of cylindrical part = πr2h
[Formula.]

= 3.14 × 92 × 16
[Substitute the values.]

= 4069.44
[Simplify.]

Volume of the cylindrical part = 4069.44 m3.

Volume of Conical part = 1 / 3πr2h
[Formula.]

= 13 × 3.14 × 92 × 25
[Substitute the values.]

= 2119.50
[Simplify.]

Volume of the cone = 2119.50 m3.

= (2119.50 + 4069.44) m3 = 6188.94 m3
Volume of air that occupies the tent = volume of cylindrical part + volume of conical part

6188.9 m3
[Round the answer to one decimal place.]

Volume of air that occupies the tent = 6188.9 m3.

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

#### Solution:

Volume of a square pyramid = 1 / 3 × base area × height
[Volume formula.]

Base area of the square pyramid = (base edge)2
[The base is a square.]

= 92

= 81 in.2
[Multiply.]

Volume of the square pyramid = 1 / 3 × 81 × 6
[Substitute base area = 81 and height = 6.]

= 162 in.3
[Simplify.]

So, the volume of the square pyramid is 162 in.3.

Correct answer : (4)
64.
Find the height of the cone whose volume is 480$\pi$ cm3 and base radius is 12 cm. a. 10 cm b. 13 cm c. 30 cm d. 20 cm

#### Solution:

Let h be the height of the cone and r be the base radius of the cone.

Volume of the cone, v = (1 / 3)πr2h
[Volume formula.]

The height of the cone, h = 3vπr2

= 3 × 480ππ×122
[Substitute v = 480π and r = 12.]

= 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 ft3 and height is 4 ft? a. 9 ft b. 8 ft c. 5 ft d. 6 ft

#### Solution:

Let r be the radius of the cone.

Volume of the cone, V = (1 / 3r2h
[Formula.]

r = 3Vπh
[Rewrite the formula.]

= 3 × 48ππ × 4
[Substitute V = 48π and h = 4.]

= 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 ft3 b. 288π ft3 c. 36π ft3 d. 96π ft3

#### Solution:

= 122= 6 ft
The base radius of the cone, r = diameter2
[Since the diameter of the cone is 12 ft.]

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

h2 + 62 = 102
[Substitute AB = h, BC = 6 ft, and AC = 10 ft.]

h2 + 36 = 100
[Evaluate powers.]

h2 = 100 - 36
[Subtract 36 from both sides.]

h2 = 64
[Subtract.]

h = 64
h = 8
[Take square root on both sides.]

The height of the cone is 8 ft.

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

= 13× π × 62 × 8
[Substitute r = 6 and h = 8.]

= 96π ft3
[Simplify the expression.]

The volume of the cone is 96π ft3.

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

#### Solution:

Base radius of the new cone = 2 × radius of the initial cone = 2 × 5 = 10 in.
[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 = 1 / 3πr2h
[Formula.]

= 3140
Volume of new cone = 1 / 3× π × 102 × 30
[Substitute the values in the formula and simplify.]

Volume of the new cone is 3140 in.3.

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 cm2? (Round the answer to the nearest whole number.) a. 1022 cm3 b. 1014 cm3 c. 1025 cm3 d. 1017 cm3

#### Solution:

Curved surface area of cone = πrl
[Formula.]

πrl = 423.9
[Since curved surface area of cone is 423.9 cm2.]

3.14 × 9 × l = 423.9
[Substitute the values of π and r.]

l = 15
[Simplify.]

Slant height of the cone (l) = 15.

Height of cone2 = slant height of cone2 - radius2.

Height of cone2 = 152 - 92
[Substitute the values.]

Height of the cone = 12 cm
[Take the square root of each side.]

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

= 1 / 3× 3.14 × 92 × 12
[Substitute the values.]

= 1017.36
[Simplify.]

1017
[Round the answer to the nearest whole number.]

Volume of the cone = 1017 cm3.

Correct answer : (4)

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