Question

Suppose a sphere, cylinder, and cone all share the same radius and 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

1 cylinder = 2 cones + 1 sphere
1 cylinder = 2 cones + 1 sphere

sphere = cylinder + cone
sphere = cylinder + cone

3 cones = 1 cylinder
3 cones = 1 cylinder

sphere - cone = cylinder

Answer 1

Let r be the common radius and h = 2r the common height for the cylinder and cone.

Volumes:
- Sphere: (4/3)πr^3
- Cylinder: πr^2h = πr^2(2r) = 2πr^3
- Cone: (1/3)πr^2h = (1/3)πr^2(2r) = (2/3)πr^3

Cylinder ÷ Cone = (2πr^3) / ((2/3)πr^3) = 3, so 1 cylinder = 3 cones.

Thus the true statement is: 3 cones = 1 cylinder.