Question

a curve is inscribed in a sphere of radius r then its volume as well as its curved surface is greater when its altitude is​

Answer 1

Answer:

Radius of sphere =r

Let ∠OAB=ϕ

So radius of cylinder, r

′

=rcosϕ

h/2=rsinϕ

h=2rsinϕ

C & A=2πr

′

h

C & A=2π(2rsinϕ)(rcosϕ)

C & A =2πr

2

sin2ϕ

C & A is maximum where sin2ϕ is max.

i.e. sin2ϕ=π/2

2ϕ=π/2

ϕ=π/4.

∴h=2rsinϕ

h=

2

r