A cylindrical hole of radius 1 is bored through a solid ball

A cylindrical hole of radius 1 is bored through a solid ball of radius 2 to from a ring coupler. Find volume and the outer surface area of this coupler.

Solution

Volume:

Volume of the sphere to be 32 pi / 3. ( V = 4/3 pi (2)^3 )

The volume of the cylinder is 4 pi. (V = pi* (1)^2 (4) )

So the volume of the sphere with hole = 32pi/3 - 4 pi = 20 pi/3.

Surfaace Area:

For surface area of the sphere with hole, the SA is 24 pi.

SA = area of sphere + lateral area of cylinder SA

= 4 pi (2)^2 + 2 pi(1) (4) SA

= 16 pi + 8 pi

= 24 pi