If a right circular cylinder of height 14 is inscribed in a sphere of radius 8

• Mensuration

If a right circular cylinder of height 14 is inscribed in a sphere of radius 8, then the volume of the cylinder is

1. 110
2. 220
3. 440
4. 660

Solution

DC is diameter of the cylinder.

∠ADC = 90°

AC is the diameter of the sphere.

Thus, AC = 16 and AD = height of the cylinder = 14

DC² = 16² – 14² = 60

If the radius of cylinder is r,

r² = 60/4 = 15

Volume of cylinder = πr²h = π × 15 × 14 = 660

The correct option is D.