WORD PROBLEMS ON VOLUME OF 3D SHAPES

	Volume of cube = a3
	Volume = lwh
	= Area of triangle x height
	Volume = (3√3/2)a2 h
	Volume = πr2h
	Volume = (1/3) base area x height
	Volume = (1/3) base area x height = (1/3)πr2h
	Volume = (4/3)πr3
	Volume = (2/3)πr3

Problem 1:

A rectangular prism has a base with a length of 25, a width of 9, and a height of 12. A second prism has a square base with a side of 15. If the volumes of the two prisms are equal, what is the height of the second prism?

Solution :

Measures of rectangle :

length = 25, Width = 9 and Height = 12

The volume of rectangle = length × width × height

= 25 × 9 × 12

V = 2700

The volume of first rectangle prism is 2700.

The volumes of the two prisms are equal.

So, the volume of the square prism V = a² h

Side a = 15

2700 = 15 × 15 × h

2700 = 225 × h

h = 2700/225

h = 12

The height of the second prism is 12.

Problem 2 :

A cube has a volume of 3375 cubic units. Calculate the length of one side of the cube.

Solution :

Volume of cube = 3375 cubic units

Volume of cube = a³

a³ = 3375

a = ∛3375

a = ∛(15 x 15 x 15)

a = 15

So, the length of one side of the cube is 15 cubic units.

Problem 3 :

The volume of a cylinder is 441π in³. The height of the cylinder is 9 in. Calculate the radius of the cylinder to the nearest tenth of a centimeter.

Solution :

Volume of a cylinder = 441π in³

The height of the cylinder = 9 in

The volume of a cylinder = πr²h

πr²h = 441 π

r²h = 441

r² × 9 = 441

r² = 441/9

r² = 49

r = 7

So, the radius of the cylinder is 7 in.

Problem 4 :

The volume of a cylinder is 794.3 cm³. The height of the cylinder is 7 cm. calculate the radius of the cylinder to the nearest tenth of a centimeter.

Solution :

Given, the volume of a cylinder = 794.3 cm³

The height of the cylinder = 7 cm

The volume of a cylinder = πr²h

πr²h = 794.3

22/7 × r² × 7 = 794.3

22 × r² = 794.3

r² = 794.3/22

r² = 36.10

r = 6 cm

So, the radius of the cylinder is 6 cm.

Problem 5 :

The volume of a cube is 216 cubic yards. Find the side length.

Solution :

Volume of a cube = 216 cubic yards

Volume of a cube V = (side)³

216 = (side)³

Side = 216

Side = 6 cubic yards

The side length is 6 cubic yards.

Problem 6 :

Julia has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an unknown height. He needs to build another rectangular prism with a length of 5 centimeters and the same height as the original prism. The volume of the two prisms will be the same. Find the width, in centimeters, of the new prism.

Solution :

The volume of rectangular prism = length × width × height

Length = 10 cm, Width = 2 cm

The volume of rectangular prism V = 10 × 2 × h

V = 20h ------(1)

The volume of new rectangular prism V

= 5 × width × height ------(2)

(1) = (2)

20 h = 5 × width × h

20 = 5 × width

Width = 20/5

Width = 4 cm

So, the new prism of the width is 4 cm.

Problem 7 :

The volume of a right cylinder is 3600π cubic centimeters and the height is 16 centimeters. Find the radius.

Solution :

Given, Volume of a right cylinder = 3600π cm³

Height = 16 cm

The volume of a cylinder V = πr²h

3600π = π × r² × 16

3600 = 16r²

r² = 3600/16

r² = 225

r = 15 cm

So, the radius of cylinder is 15 cm.

Problem 8 :

A right circular cylinder has a volume of 2,000 cubic inches and a height of 4 inches. What is the radius of the cylinder to the nearest tenth of an inch?

Solution :

Volume of a right circular cylinder = 2000 in³

Height = 4 inches

The volume of a cylinder V = πr²h

2000 = 22/7 × r² × 4

2000 = 88/7 × r²

2000 = 12.57 r²

r² = 2000 / 12.57

r² = 159.1

r = 12.6

r = 13 in

So, the radius of the cylinder is 13 in.