Hello!

Here's a question that I couldn't understand;

A canvas tent is to be constructed in the shape of a right-circular cone with the ground as base;

Using the volume V and curved surface area S of the cone,

and Find the dimensions of the cone that maximises the volume for the mē of canvas material, and find this maximum volume.

My attempt:know the two formulas: and , l, of course, is the "slant height". Using the Pythagorean theorem, l^2= r^2+ h^2.

Since we must have: , Squaring both sides of that .Now we must solve for h and replace h in V= \pi r^2h/3 by that to get a problem in just the one variable r. (Then after that we find the derivate to find the largest possible value of that function i.e. maximized.)

My problem is here: How do we solve for h in ??

Is it: ?

Thank you,

Regards