Answer:
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.
