The cylinder shown has a volume of 150 cubic inches and its height is equal to its radius. The cylinder and the sphere shown have the same radius. What is the volume of the sphere?

the volume of the sphere = 200 inches³

Step-by-step explanation:

given that

volume of a cylinder = 150 in³

height of the cylinder = the radius of the cylinder

also,

Radius of the cylinder = Radius of the sphere

volume of the sphere = ?

solution

Recall,

volume of a cylinder = πr²h

don't forget that

height of the cylinder = the radius of the cylinder

i. e h = r

150 = πr²r

150 = πr³

also,

volume of a sphere  = 4/3πr³

note that

πr³ = 150

volume of a sphere  = 4/3 x 150

volume of a sphere  = 600/150

volume of a sphere  = 200inces³

therefore the volume of the sphere is = 200inches³

the answer is 5636.7