Question

The volume of gas a balloon can hold varies directly as the cube of its radius. Imagine a balloon with a radius of 3 inches can hold 108 cubic inches of gas. How many cubic inches of gas must be released to reduce the radius down to 2 inches?

Answer 1

Answer:76

Explanation:

Answer 2

• 76 in³

Explanation:

Volume of gas varies directly as the cube of its radius.

• V = kr³

Find k:

• 108 = k(3³)
• k = 108/27
• k = 4

Volume of the smaller balloon:

• V = 4r³
• V = 4(2³) = 32 in³

The difference in volumes is the volume of released gas:

• 108 - 32 = 76 in³