Question

The cylinder has a volume of 30 cubic units. The cone and cylinder have the same height and the same base. What is the volume of the cone?

Answer 1

The volume of the cone is 10 units^3

Explanation:

step 1

Find the equation of the volume of the cylinder

we know that

The volume of a cylinder is equal to

Vcylinder=pi r^{2} h

In this problem

Vcylinder=30 units^3

so

30=pi r^{2} h-----> equation A

step 2

Find the volume of the cone

we know that

The volume of the cone is equal to

Vcone=(1/3)pi r^{2} h -----> equation B

substitute equation A in equation B

Vcone=(1/3)(Vcylinder)

Vcone=(1/3)(30)

Vcone=10 units^3