The volume of a sphere whose diameter is 18 centimeters is 246, 324, 648, or 972π cubic centimeters. If its diameter were reduced by half, its volume would be 1/2, 1/4, 1/6, or 1/8 of its original volume?

A. The correct answer is D. 972π cm³

B. The correct answer is D. 1/8

Step-by-step explanation:

1. Let's review the information given to us to answer the questions correctly:

Diameter of a sphere = 18 cm

Radius of a sphere = 18/2 = 9 cm

2. Volume of a sphere

Volume = 4/3 * π * r³

Replacing with the real values, we have:

Volume = 4/3 * π * 9³

Volume = 4/3 * π * 729

Volume = 243 * 4 * π

Volume = 972π cm³

The correct answer is D. 972π cm³

3. Volume of the sphere with diameter reduced by half

Diameter of a sphere = 9 cm

Radius of a sphere = 9/2 = 4.5 cm

Volume = 4/3 * π * r³

Replacing with the real values, we have:

Volume = 4/3 * π * 4.5³

Volume = 4/3 * π * 91.125

Volume = 364.5/3 * π

Volume = 121.5π cm³

New volume / Original volume = 121.5π/972π

New volume / Original volume = 121.5/972 = 0.125 = 1/8

The new volume is 1/8 of the original volume. The correct answer is D. 1/8