Question

A cylinder has an 18-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is
placed within the cylinder, and then the cylinder is filled with water. How much water is in the cylinder? Give
your answer in terms of pi.
1,162 in
1,179 in
1,215 in
1,251 in

Answer 1

water in cylinder = 1.179π in³

Further explanation

Volume is a derivative quantity derived from the length

The unit of volume can be expressed in liters or milliliters or cubic meters

The volume of the cylinder

V = πr².h

the volume of ball

V= 4/3πr³

volume of cylinder

$\tt V=\pi.9^2.15=1215\pi$

volume of the ball

$\tt V=\dfrac{4}{3}\pi.r^3\\\\V=\dfrac{4}{3}.\pi.3^3=36\pi$

water in the cylinder

V cylinder - V ball

$\tt 1215\pi-36\pi=1179\pi$