Question

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = √3 is

(A) 4/3(√3π)

(B) 8/3(√3π)

(C) 4π

(D) 2π

Answer 1

Answer is (C) 4π

See Fig. Volume of required cylinder = V = πr²h    (1)

Now, by Pythagoras theorem, we have

Therefore, volume is maximum when h = 2. From Eq. (1), required volume is

V = π(3 x 2 - 1/4 x 2³) = π(6 - 2) = 4