Question

the right triangle whose hypotenuse is sqrt6 m long is revolved about one of its legs to generate a right circular cone. find the radius, height, and the volume of the cone of the greatest volume that can be made.

Answer 1

sounds like calculus

Answer 2

with height h and radius r being the legs of a right triangle, you have
h^2 + r^2= 6

Volume of a cone is
V= (1/3) pi r^2 h

sub in r^2= (6-h^2) and take the derivative wrt h
Set to zero and solve for h