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?

Question

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?

campbell_st · Answer

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..

anonymous · Answer

what should I choose for the number? any?

campbell_st · Answer

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 

$$h = \frac{2r}{r + 2}$$

campbell_st · Answer

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

campbell_st · Answer

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

anonymous · Answer

ok thanks