# What is the largest lateral surface area possible for a cylinder inscribed in a cone?

The radius of the base of a right circular cone is $14$ cm and altitude $20$ cm. What is the largest lateral surface area possible for a cylinder inscribed in this cone?

Actually I've tried to solve this one. Let the height , radius of the largest possible cylinder are $h \$ and $\ r$ respectively . Then considering the upper triangle and the total triangle , it comes

$\frac{20-h}{r}=\frac{20}{14} \ => 7h+10r=140$

next what should be my approach to solve this one ?

• What have you tried so far? Given your rep, you're probably familiar enough with the site to know that if you're posting what is obviously a homework question, you should either provide something interestingly non-obvious about it, or tell us where you're having a problem dealing with the question. – stochasticboy321 Oct 13 '15 at 2:52
• edited @stochasticboy321 – ROBINSON Oct 13 '15 at 3:01
• Great. Now, you know the formula for the surface area in terms of $r$ and $h$. Feed the above relation in that to get surface area as a function of $r$. Can you find the maxima of this? – stochasticboy321 Oct 13 '15 at 3:23
• got it .. .. easy one .. thanks for help – ROBINSON Oct 13 '15 at 3:30
• You're welcome. Sorry for the rant above, and please do add some context on your question the next time, so the community can differentiate you from freeloaders who want someone to do their homework for them without having to think about it first. – stochasticboy321 Oct 13 '15 at 3:37