﻿ Find the maximum surface area of a cylinder that can be inscribed in a given sphere of radius R.   : Kaysons Education

# Find The Maximum Surface Area Of A Cylinder That Can Be Inscribed In A Given Sphere Of Radius R.

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## Question

### Solution

Correct option is

Let r be the radius and h be the height of cylinder. Consider the right triangle shown in the figure.

2r = 2R cos θ and h = 2R sin θ

Surface area of the cylinder = 2 π rh + 2 π r2

Hence surface area is maximum for θ = θ0 = 1/2 tan –1

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