He volume of a rectangular prism is 2,058 cubic cm. The length of the prism is 3 times the width. The height is twice the width.

Question

3 years ago

11

Find the height of the prism.

1 answer:

MrMuchimi · Answer 1 · 2022-05-05T11:27:01+03:00

Answer: the height of the prism is 14 cm.

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 prism is 3 times the width. It means that

L = 3W

The height is twice the width. This means that

H = 2W

Therefore,

Volume = 3W × × W × 2W = 6W³

The volume of a rectangular prism is 2,058 cubic cm. This means that

2058 = 6W³

Dividing through by 6, it becomes

343 = W³

W = 7

Therefore, the height of the prism would be

H = 2W = 2 × 7

H = 14 cm