Question

7 practice 7 (from unit 5, lesson 8)
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. what is the volume of the image?
type your answer in the box.
______ cubic units

Explanation:

Step1: Find surface area scale factor

$\text{Scale factor for surface area} = \frac{198}{22} = 9$

Step2: Find linear scale factor

$\text{Linear scale factor} = \sqrt{9} = 3$

Step3: Find volume scale factor

$\text{Scale factor for volume} = 3^3 = 27$

Step4: Calculate new volume

$\text{New volume} = 6 \times 27 = 162$

Answer:

162 cubic units