There are many ways to describe a sphere. When given certain bits of information you can find out even more than you already knew! By using formulas, you can take the small pieces of information that you have and expand them to a much broader spectrum.
When you are given a radius, you can find the surface area and the volume. The formula to find surface area is S=4πr2. However, the formula to find the volume of a sphere is V=3/4πr3.
The art industry depends on formulas for volume, area, and surface area. For example, say that an art group at Boston University needs to make a sculpture but they only have a certain amount of supplies. The plan calls for a sphere that is made out of clay. They know what the radius is and they need to find out how much the surface area is so they know how much clay to use.
By multiplying the radius by itself (squared) and pi by four and both of those products by each other then you have the surface area. When you are trying to find the surface area of a half sphere though you will have to divide all the numbers by two.
S=4πr2
2
That art group also has to know what the volume of the clay sphere will be so that when they make the clay sphere how heavy the sphere will be.
To reach the volume of a sphere you have to multiply 3/4 by pi. Then multiply that product by the radius cubed.
Say the art team decides they want to cut the sphere in half but they still want to know what the volume is. All they have to do is divide the formula by two.
V=3/4πr3
2
