Question

The length of the rectangular prism shown below is three times the width. The height and the width are the same. If the volume of the prism is 81 cubic centimeters, what is the length of the prism, in centimeters?
F. 3
G. 9
H. 18
J. 27
K. 49

Answer 1

Answer: the length of the prism is 9cm

Step-by-step explanation:

The formula for determining the volume of a rectangular prism is expressed as

Volume = length × height × width

Volume = LWH

The length of the rectangular prism is three times the width.. It means that

L = 3W

The height and the width are the same. This means that

H = W

Therefore,

Volume = 3W × × W × W = 3W³

If the volume of the prism is 81 cubic centimeters, it means that

81 = 3W³

Dividing through by 3, it becomes

81/3 = 3W³/3

W³ = 27

Taking cube root of both sides, it becomes

W = 3

Therefore, the the length of the prism would be

L = 3W = 3 × 3

L = 9 cm