# Calc1.84

Find the volume of a cylinder with radius 3 and height 10.

Here, we are finding the volume of an object with circles for cross-sections. It is quite simple since, in a cylinder, the circles are all the same size. So, the cross-sectional area at any point is just $A=\pi (3)^{2}$. Since the area does not depend on x, it does not matter which interval we integrate over so long as it has a length of 10. So the volume is

$\int _{{0}}^{{10}}9\pi \,dx=9\pi x{\big |}_{{0}}^{{10}}=90\pi \,$

Thus, the volume is $90\pi$ cubic units. This is the same answer we would get if we used the formula for the volume of a cylinder, $V=\pi r^{2}h$. This example shows that you can get the volumes of already known shapes but you can also get volumes for shapes with varying cross-sectional areas for which there is on specific formula.