Aright circular cylinder is inscribed in a sphere with diameter 4cm as shown. if the cylinder is open at both ends, find the largest possible surface area of the cylinder

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

  ( see in the below diagram ),

Thus, the surface area of the cylinder,

Differentiating with respect to r,

Again differentiating with respect to r,

For maximum or minimum,

Since, for r = √2,

Hence, the surface area is maximum if r = √2,

And, maximum surface area,