Volume of Spheres - Concept
To find the volume of a sphere, we can calculate the volume by using a simple volume formula where we multiply 4/3 by pi by the radius cubed. The volume of sphere formula is unique because it only requires the radius to calculate the volume of any sphere. When finding the volume of spheres, it is important to note if we are given the radius or the diameter of the shape. This formula is very similar to other prism volume formulas.
If you're talking about three dimensional solid that's a sphere, you can calculate its volume using the formula v=4 thirds pi times the radius cubed. Now couple of things about this formula. Most Geometry classes won't make you prove it, so I'm not going to get into that derivation. Second key things about this is notice how many variables are used in this formula. One, the only thing you need to know in order to get the volume of the sphere is its radius.
So let's look at a quick example about how we could use that formula. Here we have a sphere and we're being asked to find its volume. Now notice that what they give you is not a radius but a diameter. So we're going to start off by writing our formula, volume equals four thirds pi times your radius cubed.
Now something that you should notice is that we have r to the third which reminds you that we are talking about volume and not a surface area. So we said that r is going to be half of 12, since 12 is our diameter. So volume equals four thirds times pi times 6 cubed. Now 6 cubed if I use my calculator is 216. So we say volume is equal to four thirds pi times 216. I'm going to multiply four thirds by 216 on my calculator. I should end up with some number larger than 216 and I do.
So volume is equal to 288 pi and then we have to write in our units, cubic centimetres. So there's only one dimension you need to know in order to calculate the volume of a sphere and that is your radius. In this problem we had to divide 12 in half because there was a diameter so we could substitute and find our volume.