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
+499 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
