Question

A hole of radius r is bored through the center of a sphere of radius r. Find the volume v of the remaining portion of the sphere.

Answer 1

V=πr^2(4r/3-h), where h will be the diameter of the sphere, V=-(2πr^3)/3

Step-by-step explanation:

Answer 2

Πr²(4r/3 - h)

Step-by-step explanation:

Volume of a sphere is 4/3Πr³. If a hole of radius r is bored through, the hole with generate a circular shape in the sphere. The volume of the remaining portion of the sphere will be the difference between the volume of the sphere and the area of the hole bored(which will be volume of a cylinder since the hole bored will create a cylindrical shape in the sphere)

Area of the remaining portion = Volume of sphere - volume of a cylinder

Volume of sphere = 4/3Πr³

Volume of a cylinder = Πr²h

Volume of the remaining portion = 4/3Πr³ - Πr²h

= Πr²(4r/3 - h)

Where h is the height of the cylindrical hole