A solid has volume 6 cubic units and surface area 22 square units. the solid is dilated, and the image has a surface area of 198 square units. what is the volume of the image?

Question

asked Sep 27, 2024 219k views

1 Answer

Francesco Abeni · Answer 1 · 2024-10-03T09:52:24+0000

Answer:

162 units³

Explanation:

Original solid :

$\text{V} = 6 \ \text{units}^3$

$\text{SA} = 22 \ \text{units}^2$

Dilated solid :

$\text{V} = \ ?$

$\text{SA} = 198 \ \text{units}^2$

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
= 3^3 = 27

The dilated volume is:

$6 * 27 = 162 \ \text{units}^3$

Answer: 162 units³