A triangular prism has a base that is 6 cm by 4 cm and a height of 8 cm. If all dimensions are tripled, what happens to the volume?

A. When the dimensions are tripled, the volume is three times the original volume.

B. When the dimensions are tripled, the volume is six times the original volume.

C. When the dimensions are tripled, the volume is eighteen times the original volume.

D. When the dimensions are tripled, the volume is twenty-seven times the original volume.

Question

Elijah Holmes

Mathematics

12 January, 12:03

A triangular prism has a base that is 6 cm by 4 cm and a height of 8 cm. If all dimensions are tripled, what happens to the volume?

A. When the dimensions are tripled, the volume is three times the original volume.

B. When the dimensions are tripled, the volume is six times the original volume.

C. When the dimensions are tripled, the volume is eighteen times the original volume.

D. When the dimensions are tripled, the volume is twenty-seven times the original volume.

+4

Answers (1)

Know the Answer?

Julio Leon · Answer 1

The answer is choice D) the volume is 27 times the original

Imagine we had a rectangular block. The block has side lengths of L, W, H

The volume of which is V = L*W*H

If we triple each dimension, then we have 3L, 3W, 3H. The new volume is 3L*3W*3H = 27LWH = 27*V

This idea applies to any 3D solid. It doesn't have to be a rectangular block. The reason why is because any 3D solid can be composed of tiny little blocks to get a rough approximation.