Question

A solid has volume 6 cubic units and surface area 22 square units. The solid is dilated, and the image has surface area 198 square units.

Answer 1

162 units³

Explanation:

Original solid:

V = 6 units³

SA = 22 units²

Dilated solid:

V = ?

SA = 198 units²

The ratio of the areas is 198/22 = 9

The ratio of the area is the square of the scale factor.

The scale factor is:

scale factor = √9 = 3

The ratio of the volumes is the cube of the scale factor.

ratio of volumes = 3³ = 27

The dilated volume is:

6 × 27 = 162 units³

Answer: 162 units³