Question

A cylinder and a cone have the same base and altitude. If the volume of the cone is 30 cubic inches, what is the volume of the cylinder?

A. 10 cubic inches
B. 15 cubic inches
C. 30 cubic inches
D. 60 cubic inches
E. 90 cubic inches​

Answer 1

The volume of the cylinder is 90 cubic inches. Choice E

Explanation:

The Volume of a Cone and a Cylinder

Given a cone of radius r and height h, the volume is calculated as:

`\displaystyle V_(cone)=(1)/(3)\cdot \pi r^2h`

If we have a cylinder with the same dimensions, the volume is:

`V_(cyl)=\pi r^2h`

Substituting from the first formula:

`V_(cyl)=3V_(cone)=3*30`

`V_(cyl)=90`

The volume of the cylinder is 90 cubic inches. Choice E