Question

When the radius of a sphere is doubled, what is the resulting change in volume?

A The original volume is multiplied by 10.The original volume is multiplied by 10.
B The original volume is multiplied by 4.The original volume is multiplied by 4.
C The original volume is doubled.The original volume is doubled.
D The original volume is multiplied by 8.

Answer 1

When the radius of a sphere is doubled, the resulting change in volume is given by option D: The original volume is multiplied by 8.

The volume of a sphere is proportional to the cube of its radius. When the radius is doubled, the new volume will be 2^3 = 8 times the original volume.

Answer 2

A

Explanation:

The resulting change in volume when the radius of a sphere is doubled can be determined by examining the formula for the volume of a sphere.

The volume of a sphere is given by the formula:

V = (4/3) * π * r^3

When the radius (r) is doubled, we can substitute the new radius (2r) into the formula and calculate the new volume (V'):

V' = (4/3) * π * (2r)^3

V' = (4/3) * π * 8r^3

V' = (4/3) * π * 8 * r^3

V' = (32/3) * π * r^3

Comparing the new volume (V') with the original volume (V), we can see that the new volume is multiplied by a factor of (32/3) when the radius is doubled.

Therefore, the correct answer is:

A The original volume is multiplied by 32/3.