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

2 cylinders = 1 cone
2 cylinders = 1 cone

2 cones = 1 sphere
2 cones = 1 sphere

2 cones = 1 cylinder
2 cones = 1 cylinder

2 spheres = 1 cone

Answer 1

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

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

Then 2 × (cone) = 2 × (2/3)πr^3 = (4/3)πr^3 = sphere.

So: 2 cones = 1 sphere.