Problema Solution
A cylinder has a volume of 24 cubic centimeters. The height of a cone with the same radius is two times the height of the cylinder. What is the volume of the cone?
Answer provided by our tutors
let
V1 = 24 cm^2 the volume of the cylinder
r1 = the radius of the cylinder
h1 = the height of the cylinder
V1 = r1^2 * pi * h1 the volume of the cylinder
for the cone we have
r2 = r1 the radius of the cone
h2 = 2h1 the height of the cone
V2 = the volume of the cone
V2 = (1/3) * r2^2 * pi * h2
V2 = (1/3) * r1^2 * pi * 2h1
V2 = (1/3)*2 * r1^2 * pi * h1
V2 = (2/3) V1
V2 = (2/3)*24
V2 = 16 cm^3 is the volume of the cone.