Question

A ball of radius 17 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.

Answer 1

Answer:

19,133.067

Step-by-step explanation:

Volume of the ball (spherical in nature) Vb = 4/3πrb³

Volume of the hole Vh = 4/3πrh³

rb is the radius of the ball

rh is the radius of the hole

If a ball of radius 17 has a round hole of radius 7 drilled through its center, the volume of the resulting solid will be expressed as:

V = Vb - Vh

V = 4/3πrb³ - 4/3πrh³

factor out the like terms;

V = 4/3π(rb³-rh³)

Given

rb = 17

rh = 7

V = 4/3π(17³-7³)

V = 4/3π(4913-343)

V = 4/3π(4570)

V = (4π*4570)/3

V = 57,399.2/3

V = 19,133.067

Hence the volume of the resulting solid is 19,133.067