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)
Responses

24 cm3

24 cm cubed

54 cm3

54 cm cubed

12 cm3

12 cm cubed

18 cm3

Answer 1

Cylinder volume V_cyl = πr^2h. Given h = 2r, so V_cyl = πr^2(2r) = 2πr^3 = 36 ⇒ r^3 = 36/(2π) = 18/π.

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

Answer: 24 cm^3.