Question

A cylinder has a height of 4 inches greater than the radius of its base. Find the radius and the height to the nearest inch if the volume of the cylinder is 5pi cubic inches.

Answer 1

d

Explanation:

just cus

Answer 2

`h=5in, r=1in`

Explanation:

The volume of a cylinder is:

`V=\pi*r^2*h`

where
`r` is the radius and
`h` is the height.

The height is 4 inches greater that the radius, so:

`h=r+4in`

Substituting this in the formula for volume:

`V=\pi*r^2*(r+4)`

the volume is
`V=5\pi in^3`

thus:

`5\pi in^3=\pi*r^2*(r+4in)`

Dividing everything between pi:

`5in^3=r^2*(r+4in)`

`5in^3=r^3*+4r^2`

We can see that the solution for this is
`r=1in`

since
`(1)^3*+4(1)^2=1+4=5`

We have the radius, now we find the height:

`h=r+4in=1in + 4in = 5in`

`h=5in, r=1in`