Four spheres of a radius 6cm just fit inside a cylinder

calculate the volume inside the cylinder that is empty

leave your answer in terms of π

diameter=12cm

The space left inside the cyclinder = 36π (h - 24)

step-by-step explanation:

Radius of sphere = 6cm

Diameter of cylinder = 12cm

Radius of cylinder = d / 2 = 12 / 2 = 6cm

Formula for volume of a sphere = 4/3 πr³

Formula for volume of volume of a cylinder = πr²h

r = radius

h = height

The volume of one sphere = 4/3πr³

Volume of 4 spheres = 4 * 4/3πr³ = 12/3 πr³ = 4πr³

But radius of the sphere = 6cm

Volume of the sphere = 4 * π * 6³

Volume of the sphere = 864π

Let the space left in the cylinder = x

The space left in the cylinder (x) = volume of the cylinder - total volume of the spheres

x = πr²h - 4πr³

Note : both radius = 6cm and we can just substitue it

x = πr² (h - 4r)

x = π*6² (h - 4*6)

x = 36π (h - 24)

The space left inside the cylinder = 36π (h - 24) since we don't know the value of the height of the cylinder.