How to Calculate the Surface Area and Volume of a Sphere

Geometry can be one of the most confusing years of math that you will encounter in high school. With all the different shapes, types of angles and formulas to remember you may start to feel that you are swimming in a sea of confusion. Ease your confusion by learning how to calculate the surface area and volume of a sphere.

Things You'll Need

• Paper
• Pencil
• Calculator

Instructions

Surface Area of a Sphere

1. Learn that the surface area of a sphere can be expressed by the equation A=4π(r^2). In this equation, the letter A stands for the surface area of a sphere and the letter r stands for the radius of the sphere, or the distance from the center of the sphere to the edge of the sphere.

2. Use the order of operations to work through calculating the surface area of the sphere. You can remember the order of operations by using the made up word, PEMDAS, where each letter stands for a different mathematical operation. The first operation that you should perform in any equation is an operation that is inside a set of parentheses. Once you are finished with the parentheses you move to exponents. After exponents come multiplication and division, either of these two operations can be performed before the other. Once you have completed all multiplication and division in a given equation you finish up with addition and subtraction and like multiplication and division, either of these two operations can be performed before the other.

3. Start by calculating the radius squared of the sphere that you are working with because that is what the order of operations calls for. For example, if you want to determine the surface area of a sphere with a radius of 4 inches, then the first thing you would need to do is calculate 4^2, which is 16.

4. Multiply out 4π(r^2). It doesn't matter what you multiply by what first, you just need to multiply it all out to get the surface area of the sphere. In our example you would multiply out 4π16. You can start by multiply 4*16 if you want to keep your answer in terms of π. If you don't want to keep your answer in terms of π, then you can begin by multiplying any two of the three numbers together. In this example, start by multiplying 4 and 16. So, 4*16=64. Then you would multiply that by π, 64π=201.062 when you round to the nearest thousandth.

5. Put your answer in terms of units squared. So, for our example your final answer would be 201.062 inches squared is the surface area of a sphere with a 4 inch radius.

Volume of a Sphere

1. Learn that the volume of a sphere can be expressed with the equation, V=(4π(r^3))/3. In this equation, the letter V stands for the volume of the sphere and the letter r stands for the radius.

2. Use the order of operations to work through calculating the surface area of the sphere. Your can remember the order of operations by using that made up word again--PEMDAS for parentheses, exponents, multiplication, division, addition and subtraction.

3. Start be calculating the radius cubed. Since this is the innermost set of parentheses, this is the first operation that we need to perform in solving this equation according to the order of operations. Now, if you wanted to know the volume of the sphere that you just calculated the surface area for, then you would need to calculate 4^3, since the radius of that sphere is 4 inches. So, 4^3=64.

4. Keep working inside the parentheses. The next operation inside a set of parentheses that we need to do is to multiply out 4π64. Like before, you can multiply this out in any order that you wish. For this example, start by multiplying the 4 and the 64, 4*64=256. Then you'll want to multiply this answer by π, 256π=804.248 is what you get when rounding to the nearest thousandth.

5. Divide your answer by 3. Now that you have completed all the operations inside parentheses, the next and final operation that you'll need to carry out is to divide your answer from the previous step by 3, thus 804.248/3=268.083.

6. Finally put your answer in terms of units cubed. So, for this example, your final answer would be 268.083 inches cubed.