In: Math
A right triangle whose hypotenuse is √18 m long is revolved about one of its legs to generate a right circular cone. Find the radius, height, and volume of the cone of greatest volume that can be made this way.
Consider a right triangle with hypotenuse and length of other two sides .
Let the triangle is revolved about the leg of length .
The resulting cone has radius and height .
We have .
The volume of the cone is
The volume is maximum when,
The maximum volume is
Radius is and height .