A right triangle whose hypotenuse is √18 m long is revolved about one of its legs...

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.

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Expert Solution

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 .

milcah answered 1 year ago

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