Question

Two similar cylinders have surface areas of 20π square feet and 90π square feet. What is the ratio of the height of the large cylinder to the height of the small cylinder?

Answer 1

Answer:

Explanation:

Let the height of the small cylinder be h

Let the radius of the small cylinder be r

The surface area of the small cylinder is:

$SA_{small}=2\pi r(r+h)$

Simplify the expression by setting SA = 20π

$\begin{gathered} 20\pi=2\pi r(r+h) \\ \\ \frac{20\pi}{2\pi}=r(r+h) \\ \\ 10=r(r+h).........(1) \end{gathered}$

Let the height of the large cylinder be H

Let the radius of the large cylinder be R

The surface area of the large cylinder will be:

$\begin{gathered} SA_{large}=2\pi R(R+H) \\ \\ 90\pi=2\pi R(R+H) \\ \\ \frac{90\pi}{2\pi}=R(R+H) \\ \\ 45=R(R+H).......(2) \end{gathered}$

Divide equation (2) by equation (1)

$\begin{gathered} \frac{45}{10}=\frac{R(R+H)}{r(r+h)} \\ \\ 4.5=\frac{R(R+H)}{r(r+h)} \\ \\ \\ \end{gathered}$