Question

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

Answer 1

Sample response: 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.

Explanation:

edge 2021

Answer 2

volume = length * width * height
If we take the volume of the original prism we get

4m * 6m * 10m = 240m³

If we double each dimension of the prism we get

8m * 12m * 20m = 1920m³

now we divide the new volume by the old to see how much it has changed

1920m³/240m³ = 8m³

If the dimensions of the prism are doubled, the volume increases by 8 times the original number