Volume of a Sphere

Have you ever wondered how big Planet Earth really is? Our planet looks like the shape of a sphere, a common three-dimensional shape. To find out how much space is inside a sphere, we can follow the steps to find the 'Volume of a Sphere'. The formula used is four-thirds, multiplied by pi, multiplied by the radius cubed. The radius of a sphere is the distance from the middle to the outside rim of the sphere. But, before we find out the volume of the earth, let's scale it down and start with something smaller; a desk top globe. We are going to find the volume of the sphere and round the solution as stated in the directions. Always start by writing down the formula you are using. Next, identify the radius of the sphere, which will be your r value. We can substitute the value of r right into our formula, like this! Seven to the third power is three hundred forty-three, which can be multiplied by the four-thirds. The product is four hundred fifty-seven and three repeating. Next, using a calculator we will find the product of this number and pi. When rounded to the nearest tenth, the volume is approximately one thousand four hundred thirty-six and eight tenths. And don't forget to add on your units, inches cubed. Let's practice another example! Let's find the volume of this orange! When the directions say in terms of pi, it means we will not be calculating the pi on the calculator, but rather leaving it as pi. Before starting, write down the formula for the volume of a sphere. What is the radius of this sphere? Three centimeters! Substitute this value for the r and then evaluate. What is three-to-the-third power, multiplied by four-thirds? It is thirty-six, pi, which is a precise measurement since we did not round. And like the last one, don't forget to add your units, in this case centimeters cubed. Find the volume of the basketball in cubic centimeters. Pause the video here to find the volume, and press play when you are ready to check your solution. Write down the formula first! This time, we have the diameter and not the radius. The radius is half of the diameter, so here it is twelve centimeters. Volume equals four thirds, times pi, times twelve cubed. The product of four-thirds and twelve to third power is two thousand, three hundred four, pi. The volume of the basketball is approximately seven thousand, two hundred thirty-eight and two-tenths centimeters cubed. To summarize, the volume of a sphere measures the space INSIDE, and to calculate, we use the formula volume equals four thirds, times pi, times the radius cubed. Since we now have practiced, let's see if we can answer the question, what is the volume of planet earth? "Wait, this just in! The Earth may look like a sphere, but it is actually not a perfect sphere and is considered to be more of an ellipsoid." Our earth is constantly changing, therefore its size is also ever changing. But we can still estimate! The volume of the earth is approximately two hundred sixty-eight billion, eighty-two million, five hundred seventy-three thousand, one hundred six cubic miles.