Question

Suppose a sphere, cylinder, and cone all share the same radius. The cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone?(1 point)
Responses

cone = sphere − cylinder
cone = sphere − cylinder

cylinder = sphere − cone
cylinder = sphere − cone

sphere = cylinder + cone
sphere = cylinder + cone

cone = cylinder − sphere

Answer 1

Compute volumes with radius r and height h = 2r:

- Sphere: V_s = (4/3)πr^3
- Cylinder: V_cyl = πr^2(2r) = 2πr^3
- Cone: V_cone = (1/3)πr^2(2r) = (2/3)πr^3

Then cylinder − sphere = (2 − 4/3)πr^3 = (2/3)πr^3 = V_cone.

So the correct relation is: cone = cylinder − sphere.