Question

A rectangular prism has a base that is 4 m by 6 m and a height of 10 m. If all dimensions are doubled, what happens to the volume? Explain the steps that you take to arrive at your answer.

Answer 1

Answer:

Start by calculating the volume of the original prism. The area of the base, B, is 4(6) = 24 m2. Multiply that by the height to get the volume: 24(10) = 240 m3. Now, if you double all of the dimensions, you would have a rectangular prism with a base that is 8 m by 12 m and a height of 20 m. The area of the base, B, is 8(12) = 96 m2. Multiply that by the height to get the volume: 96(20) = 1,920 m3. To compare, look at the ratio of the original prism to the new prism: 96/1,920 = 1/8. The volume increases by 8 times the original volume.

Step-by-step explanation:

Sample response

Answer 2

When the dimensions of a rectangular prism will be doubled, its volume won't only be doubled but it will be 8 times as much.

The original volume of the rectangular prism is LxWxH.

V= LxWxH
V= (6m) (4m) (10m)
V= 240m³

If we double the dimensions, the volume would be

V= 2L x 2W x 2H
V= 2 x 6m x 2 x 4m x 2 x 10m
V= 2 x 2 x 2 x 6m x 4m x 10m
V= 2³ (6m x 4m x 10m)
V= 2³ x 240m³
V = 8 x 240m³
V= 1920 m³

The new volume now is 1,920 m³, which makes the rectangular prism larger than the original.