Question

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?

Answer 1

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