A cylinder has 18 inch diameter and is 15 inches tall it is filled to the top with water a 6 inch diameter ball is in place within the cylinder and then cylinder is filled with water. How much water is in the cylinder? give your answer in terms of pi

Guest Mar 24, 2020

#1**+1 **

The formula for volume of a cylinder is as follows:

given *r* as the area of one of its circular bases, and *H *as the height,

the volume of the cylinder = \(\pi*r^2*h\)

The volume of the cylinder given in this problem has an 18 inch diameter, meaning the radius is 9

The volume is then:

\(\pi * 9^2 * 15 = 1215\pi\) in.^{3}

Next, to calculate how much total water is within the cylinder, we just need to subtract the volume of the 6 inch diameter ball from the cylinder(since that ball takes up volume).

The volume of a sphere is as follows:

given *r *as its radius, its volume is then:

\(\frac43 * \pi * r^3\)

We are given that the diameter of this ball is 6 inches, so the radius is then 6/2 = 3 inches

The volume is then:

\(\frac43 * \pi * 3^3 = \frac43 * 27 * \pi = 36\pi\) in.^{3}

Our total volume of water is then:

\(1215\pi - 36\pi = 1179\pi\)in.^{3}

jfan17 Mar 24, 2020