Aright triangle whose hypotenuse is startroot 7 endroot7 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.

The maximum volume of cone is 138.25 m³

m

m

Step-by-step explanation:

A right circular cone whose hypotenuse is m

It is revolved about one leg to generate a right circular cone.

Let radius be r m and height be h m

For right angle triangle,

Volume of generated cone

Differentiate w.r.t h

For maximum/minimum

Using double derivative test

At  

so get maximum volume.

Dimension of cone:

m

m

The maximum volume of cone is 138.25 m³

b

step-by-step explanation:

x + 4/7

step-by-step explanation:

use cymath