# Finding the Volume and Surface Area of a Sphere

## Volume and Surface Area of a Sphere

Volume is the space that a figure occupies. The volume of a sphere is found by multiplying \(\frac{4}{3}\) times pi times the radius cubed. The radius is a segment that goes from the center of the sphere to a point on the outside of the sphere. Surface area is the area of the complete surface of the sphere and it’s found by multiplying 4 times pi times radius squared. Let’s look at an example.

Find the volume and the surface area of the following sphere in terms of pi and to the nearest whole number. We’ll start with volume. First we’ll write our formula for volume which is \(\frac{4}{3}\) times pi times radius cubed. Then we’ll substitute our radius which is given here as 6-feet. Volume is \(\frac{4}{3}\) times pi times 6 feet cubed. The volume is \(\frac{4}{3}\) times pi times 6 feet cubed. 6 times 6 is 36 times 6 is 216 feet cubed. \(\frac{4}{3}\) of 216 is 288. The volume is 288 pi feet cubed.

That’s our answer in terms of pi. To find it to the nearest whole number, simply multiply times pi. 288 times pi is 905 feet cubed. Now to find our surface area. The surface area is found by multiplying four times pi times radius squared.

Now we need to simplify or substitute six-feet for our radius. 4 pi times our radius is 6 feet squared. We follow PEMDAS. We need to do 6 feet squared first. 6 feet squared is 36 feet squared. 4 times pi times 36 feet squared. Then 4 times 36 feet squared is 144 pi feet squared. That’s our answer in terms of pi. Then to find it to the nearest whole number, we need to multiply times pi which gives us 452 feet squared.