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.

The volume is multiplied by 8.

Step-by-step explanation:

In order to find out what happens to the volume when the dimensions are doubled, let's find the original volume first. Then we can double the dimensions and find the new volume and compare the new volume with the original volume.

To find volume, we have to multiply base * width * height.

Let's find the original volume.

4 * 6 * 10 = 240

The original volume is 240 m.

Now, let's double the dimensions.

4*2 = 8   6*2 = 12   10*2 = 20

Let's find the new volume.

8 * 12 * 20 = 1, 920

The new volume is 1,920.

To compare the two volumes, let's divide the new one by the original.

1920/240 = 8

When the dimensions were doubled, the volume was multiplied by 8.

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

a) t'(-3, 6) and v'(0, 3)  

step-by-step explanation: