Question

Use the relationship among the formulas for the volumes of cones, cylinders, and spheres to solve the following problem. The volume of a cylinder is 36 cm3
. What is the volume of a sphere if its radius is the same as the cylinder’s and the height of the cylinder is equal to the sphere’s diameter?(1 point)

24 cm3


18 cm3


54 cm3


12 cm3

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Answer 1

Let the common radius be r. Cylinder volume = πr^2h with h = 2r, so 36 = πr^2(2r) = 2πr^3 ⇒ r^3 = 18/π.

Sphere volume = (4/3)πr^3 = (4/3)π(18/π) = (4/3)·18 = 24 cm^3.

Answer: 24 cm^3.