Question

The areas of the bases of similar rectangular prisms are 25 square inches and 64 square inches.

What is the ratio of the volumes of the rectangular prisms?


5 to 8

15 to 24

75 to 192

125 to 512

Answer 1

ratio of areas

• 25/64

Ratio of sides

• √25/64
• 5/8

Ratio of volumes

• (5/8)³
• 125/512

Option D

Answer 2

• D. 125 to 512

Explanation:

The ratio of the areas of the bases:

• 25/ 64

This is a square of the scale factor:

• k² = 25/64

The scale factor is:

• k = √25/64 = 5/8

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

• k³ = (5/8)³ = 125 / 512

Correct choice is D