Question

Samuel cut a cone from a piece of wood shaped as a cylinder. He measured the circumference of the base of the cylinder and found that it measured 3πinches. The height of the cylindrical piece of wood was 6 inches. What is the approximate volume of Samuel's cone if it has the same base area and height as the cylinder?

Answer 1

The approximate volume of the cone is 14 cube inches.

Explanation:

Circumference of the base of the cylinder = 3π inches

Height of the cylindrical piece of wood = 6 inches

volume of a cone =
`(1)/(3)`
`\pi`
`r^(2)`h

But,

circumference = 2πr

3π = 2πr

r =
`(3)/(2)`

= 1.5 inches

Radius of the base of the cylinder is 1.5 inches.

So that;

volume of cone =
`(1)/(3)` x
`(22)/(7)` x
`((3)/(2)) ^(2)` x 6

=
`(1)/(3)` x
`(22)/(7)` x
`(9)/(4)` x 6

= 14.143

volume of cone = 14.143 cube inches

The approximate volume of the cone is 14 cube inches.