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

sphere = cylinder + cone
sphere = cylinder + cone

cone = cylinder − sphere
cone = cylinder − sphere

cone = sphere − cylinder
cone = sphere − cylinder

cylinder = sphere − cone

Answer 1

Compute with radius r and height h = 2r.

Sphere: V_s = (4/3)πr^3
Cylinder: V_cy = πr^2·h = πr^2·2r = 2πr^3
Cone: V_co = (1/3)πr^2·h = (1/3)πr^2·2r = (2/3)πr^3

Now cylinder − sphere = 2πr^3 − (4/3)πr^3 = (6/3 − 4/3)πr^3 = (2/3)πr^3 = cone.

So: cone = cylinder − sphere.