Question

Jack knows the surface area of a cylinder and its radius. He wants to find the cylinder's height. He needs to rewrite the formula a=2pi r(r+h) to find the cylinder's height (h) in terms of the cylinder’s surface area (A) and its radius (r). Which is the correct formula?

A h=r+a/2pir
B h=a/2pir
C a/2pir -r^2
D a/2pir -r

Answer 1

Look at the attached formula (the one on the right).

Answer 2

(D)
`\frac{a}{2{\pi}r}-r=h`

Explanation:

It is given that Jack considers the formula for the surface area of the cylinder and its radius, the formula is:

`a=2{\pi}r(r+h)` where h is the height of the cylinder and r is the radius of the cylinder.

Upon solving the formula, we have

`a=2{\pi}r(r+h)`

`a=2{\pi}r^2+2{\pi}rh`

`a-2{\pi}r^2=2{\pi}rh`

`\frac{a-2{\pi}r^2}{2{\pi}r}=h`

`\frac{a}{2{\pi}r}-r=h`

which is the required correct formula for the height of the cylinder.

Hence, option D is correct.