## anonymous one year ago Lab is to find the radius and height of a right circular cylinder where the surface area and volume are the same number. Is there a solution? Is there more than one?

1. campbell_st

well the surface area is $SA = 2\pi r^2 + 2\pi r h$ and the volume is $V = \pi r^2 h$ so if they are equal to the same number $\pi r^2 h = 2\pi r^2 + \pi r h$ and then work from there..

2. anonymous

what should I choose for the number? any?

3. campbell_st

so if you have $\pi r^2 h = 2 \pi r^2 + 2 \pi r h$ divide every term by $\pi r$ then $rh = 2r + 2h$ make h the subject $h( r -2) = 2r$ then $h = \frac{2r}{r + 2}$

4. campbell_st

that's my best guess at this question... so r > 0

5. campbell_st

so as r gets large it looks like h gets closer to 2...

6. anonymous

ok thanks