# Finding the Volume and Surface Area of a Right Circular Cylinder

## Volume and Surface Area of a Right Circular Cylinder

Volume is the space that a figure occupies. To find the volume of a right circular cylinder, multiply the area of the base, which is a circle PI r squared, times the height of the cylinder. To find the surface area of a cylinder, which is the area of the surfaces of the cylinder, find the lateral area or the area around the side of the cylinder by multiplying two times pi times the radius times the height. Then add the areas of the bases, which are circles. Two times PI R squared because there are two bases, two circles. Let’s look at this example.

Find the volume and surface area of the following right circular cylinder in terms of pi and to the nearest whole number. We’ll start with volume. First, we’re going to write our formula down. The volume of a cylinder is found by multiplying pi times the radius squared times the height of the cylinder. Then we need to substitute our values. Volume is pi times the radius is the distance from the center to the outside of your circular base. Three feet squared times the height of the cylinder eight feet.

We need to simplify using order of operations so we’re going to square our three feet firs. Volume is three feet squared is nine. Nine feet squared times eight feet is 72 pi feet cubed. The feet cubed came from squaring feet squared here and then times feet. Feet squared times feet, feet cubed. That gives us the answer the first way which is in terms of pi meaning we don’t multiply times pi. Pi must stay in our answer. Then to find it to the nearest whole number, we do multiply times pi. 72 times pi is 226 feet cubed. These would be our two answers for volume of our cylinder.

Now for surface area. Surface area is two times pi times the radius times the height plus two times pi times radius squared. Then we substitute our values. Surface area is two times pi times the radius, three feet, times the height, eight feet, plus two times pi times the radius three feet squared. Now we need to simplify. The surface area is three feet times eight feet is 24 feet squared, times 2 is 48 feet squared, times pi, 48 pi feet squared, plus starting with three feet squared. Three feet squared is nine feet squared times two. 18 feet squared times pi 18 pi feet squared.

Then we can combine our like terms. 48 pi feet squared plus 18 pi feet squared. That gives us 66 pi feet squared. There’s our answer in terms of pi. Then to find it to the nearest whole number, we need to multiply times pi. 66 times pi is 207 feet squared. There’s our surface area in terms of pi and to the nearest whole number