Problema Solution
Mindy is a sculptor. She has a cylinder of stone with a radius of 1.5m and a height of 2m. She needs to carve out a sphere of radius 0.5m from the cylinder.
How much stone will Mindy cut away from the cylinder in order to be left with the sphere?
Answer provided by our tutors
the volume of the cylinder is:
V1 = r1^2 pi h
r1 = 1.5 m the radius of the cylinder
h = 2 m the height of the cylinder
V1 = 1.5^2 pi * 2
V1 = 9/2 pi
V1 = 4.5 pi m^3
the volume of the sphere is:
V2 = (4/3) r2^3 pi
r2 = the radius of the sphere
V2 = (4/3) 0.5^3 pi
V2 = (1/6) pi m^3
Mindy must cut off V1 - V2 of the cylinder to get the sphere or:
V1 - V2 = (9/2) pi - (1/6) pi
V1 - V2 = ((9/2) - (1/6))pi
V1 - V2 = 13/3 pi
V1 - V2 = 4 1/3 pi
V1 - V2 = 13.61 m^3
Mindy will cut away 13.61 m^3 stone in order to be left with sphere.