Question

Consider a sphere with the same radius (r = 6) as the cone shown. What is the difference in the volume between the cone and sphere? (in terms of π)

Responses
A. The volume of a cone and sphere with the same radius (r = 6) is equal.
B. The volume of the cone is 204π cm larger than the volume of the sphere.
C. The volume of the sphere is 204π cm larger than the volume of the cone.
D The volume of the sphere is 288π cm larger than the volume of the cone.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the cone, we use the formula Vcone = (1/3)πr^2h, where r = 6 and h = 12.

Vcone = (1/3)π(6)^2(12)
Vcone = 144π

To find the volume of the sphere, we use the formula Vsphere = (4/3)πr^3, where r = 6.

Vsphere = (4/3)π(6)^3
Vsphere = 288π

Therefore, the difference in volume between the cone and sphere is:

Vsphere - Vcone = 288π - 144π = 144π

Therefore, the correct answer is:
B. The volume of the cone is 144π cm larger than the volume of the sphere.