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:

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.