Final answer:
The volume of the new sphere, after the radius is doubled, is 96π cubic inches. This is calculated by multiplying the original volume by 8, since doubling the radius results in an eightfold increase in volume due to the cubic relationship. The correct answer from the given options is thus C. 96π cubic inches.
Step-by-step explanation:
The student asked how the volume of a sphere changes if its radius is doubled. To solve this, we use the formula for the volume of a sphere: V = 4/3 πr³. Given that the original volume is 12π cubic inches, when the radius is doubled, the new equivalent radius will be raised to the third power in the volume formula, meaning the new volume will be 8 times larger than the original volume because (2³) = 8. Therefore, the volume of the new sphere will be 8 × 12π cubic inches, which equals to 96π cubic inches.
The correct answer from the given options is thus C. 96π cubic inches.