A sphere is completely contained within a cylinder, with the height and diameter of the cylinder matching the diameter of the sphere. Given that the volume of the sphere is 36π cm3, what is the volume of the vacant space inside the cylinder?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 18π cm3.
Volume of sphere = 36π
Let the radius of the cylinder = Radius of sphere = r cm
(4/3)πr3 = 36π
⇒ r3 = 27
⇒ r = 3 cm
Radius of cylinder = 3 cm
Volume of cylinder = πr2h = π × 32 × 6 = π × 9 × 6 = 54π
Vacant space = 54π − 36π = 18π cm3