Question

The volume of a prism changes from 20 to 540 after a dilation. what was the scale factor of the dilation?

Answer 1

The scale factor is 3 : 1.

Explanation:

We know that,

The scale factor of the dilation of a prism is the cube root of the ratio of the volume of resultant prism after dilation and the volume of the given prism,

Here, the volume of prism before dilation = 20 cube unit,

And, the volume of the prism after dilation = 540 cube unit,

Thus, by the above statement,

`\text{The scale factor of dilation}=\sqrt[3]{(540)/(20)}`

`=\sqrt[3]{27}`

`=3`

Hence, the scale factor is 3 : 1.

Answer 2

Scale factor is used by architects or engineers to transfer their prototype idea to large-scale use. If the volume of a prism is 20, you need to multiply its dimensions with a scale factor to find the new volume which is 540. For example, if the volume is doubled, this means you used a scale factor of 2. Hence, you just have to divide the new volume by the smaller volume.

Scale factor = 540/20
Scale factor = 27