Question

A solid has volume 2 cubic units and surface area 10 square units. The solid is dilated, and the image has volume 128 cubic units. What is the surface area of the image?

Answer 1

The surface area of the image after dilation can be found by multiplying the original surface area by the dilation factor, which is 4.

Step-by-step explanation:

To find the surface area of the image after dilation, we can use the concept of similar figures.

Since the volume of the solid is dilated by a factor of 128/2 = 64, the lengths of the sides are dilated by a factor of 4 (since 4^3 = 64).

Therefore, the surface area is also dilated by a factor of 4.

So, the surface area of the image after dilation is 10 x 4 = 40 square units.