A cone-shaped drinking cup is drawn from the side view.

$\"\"$

Observe the figure.

From the pythagorean theorem,

$\"\"$

The volume of the cone is $\"\"$ .

But volume of the cone is $\"\"$ cm³.

$\"\"$

The surface area of the cone is $\"\"$ .

Squaring on each side.

$\"\"$

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

The volume of the cone is maximum when its first derivative becomes zero.

Equate $\"\"$ to zero.

$\"\"$

The height of the cone is $\"\"$ cm.

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Therefore the radius of the cone is $\"\"$ cm.

The height of the cone is $\"\"$ cm.

The radius of the cone is $\"\"$ cm.