The volume of a right circular cone is pi/3 r^2 h and it surface area is S = pi r (sq.rt.) r^2 + h^2?

Question

Find the dimensions of the cone with surface area 1 and maximal volume.

"r" is the center of cone to the edge of the cone at the base

"h" is the height of the cone

*This forms a right angle.

Answer 1

You have the wrong equations.

pi r (sq.rt.) r^2

I interpret as

πr√(r²) or πr*r or πr² which is correct for the area of the base, but why would you express it that way?

the h² term is incorrect

Volume is correct.

Correct equations are:

   surface area A = πr² + πrs where s is slant height

   volume V =  Ã¢Â…“Ï€r²h, h is height of cone (not slant)

      h² + r² = s²

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