Question

A hemisphere of radius 9 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.
radius=
height=

Answer 1

Answer:

The radius and height of the cylinder of maximum volume is 9 unit and 9 unit.

Step-by-step explanation:

Given that,

Radius = 9

According to figure,

Radius of cylinder = Radius of hemisphere

Center of cylinder base is also center of sphere.

Circular top of cylinder touching the top of hemisphere.

So, Height of cylinder = radius of hemisphere

$h = r$

$h = 9\ unit$

Hence, The radius and height of the cylinder of maximum volume is 9 unit and 9 unit.