# Thread: volume of cylinder to area?

1. ## volume of cylinder to area?

The top and bottom of the cylinder's area is found via Pi*r2
the lateral surface if found 2*pi*h
Volume = pi* radius2 * h

I am only given volume, = 500cm3
Also for each square cm of the top and bottom its 10 cents to make, and for the lateral surface its 7 cents to make.

I don't know where to make the connection with all the information to formulate a formula for r to cost; C(r)=

2. ## Re: volume of cylinder to area?

Originally Posted by blondedude092
The top and bottom of the cylinder's area is found via Pi*r2
the lateral surface if found 2*pi*h
Volume = pi* radius2 * h

I am only given volume, = 500cm3
Also for each square cm of the top and bottom its 10 cents to make, and for the lateral surface its 7 cents to make.

I don't know where to make the connection with all the information to formulate a formula for r to cost; C(r)=
First of all, the lateral surface area is actually \displaystyle \begin{align*} 2\pi \, r \, h \end{align*}, not \displaystyle \begin{align*} 2 \pi \,h \end{align*}

You are told the volume is \displaystyle \begin{align*} 500\,\textrm{cm}^3 \end{align*}, so

\displaystyle \begin{align*} \pi \, r^2h &= 500 \\ h &= \frac{500}{\pi \, r^2} \end{align*}

Now you know that the lateral surface area is

\displaystyle \begin{align*} 2\pi\,r\,h &= 2\pi\,r\left(\frac{500}{\pi \, r^2}\right) \\ &= \frac{100}{r} \end{align*}

and the area of the circular ends are each \displaystyle \begin{align*} \pi\,r^2 \end{align*}, so their areas together are \displaystyle \begin{align*} 2\pi \,r^2 \end{align*}.

Since you know it costs 10c for each square centimetre for the top and bottom, and 7c for each square centimetre of the lateral surface area, the cost, in dollars, is

\displaystyle \begin{align*} C &= 0.10\left(\frac{100}{r}\right) + 0.07\left(2\pi\,r^2\right) \\ &= \frac{10}{r} + \frac{7\pi}{ 50r^2} \\ &= \frac{500 r + 7\pi}{50r^2} \end{align*}

3. ## Re: volume of cylinder to area?

Thanks! I was trying to figure out this for hours already.