A ball of radius 16 has a round hole of radius 4 drilled through its center. Find the volume of the resulting solid.
To find the volume of the resulting solid, we need to subtract the volume of the hole from the volume of the ball.
The volume of a ball is given by the formula V = (4/3) * π * r^3, where r is the radius of the ball.
So, the volume of the ball = (4/3) * π * (16^3) = (4/3) * π * 4096 = 17408π
The volume of the hole can be calculated using the same formula, with the radius of the hole.
So, the volume of the hole = (4/3) * π * (4^3) = (4/3) * π * 64 = 256π
Now, we can subtract the volume of the hole from the volume of the ball:
Volume of the resulting solid = Volume of the ball - Volume of the hole
= 17408π - 256π
= (17408 - 256)π
= 17152π
Therefore, the volume of the resulting solid is 17152π cubic units.