How to Find the Area of a Circle Given the Diameter | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to find the area of a circle given the diameter now remember area is the amount of space a 2d figure takes up and we can measure in square units so how many square units does a given figure take up or you can think of it as how many square units to cover the given figure now the formula we use for the area of a circle is area equals pi r squared so pi times the radius squared so we do need to be familiar with both diameter and radius when we work with circles diameter is the distance all the way across a circle so it's a line segment that connects two points on the circle and it has to go through the center and then the radius is half the diameter so it goes from the center to any point on the circle and then lastly before we get into our example is pi which is the ratio of a circle's circumference to its diameter pi is a constant so it's the same for all circles now pi is irrational it goes on forever so we are going to use an approximate or rounded version of pi 3.14 with that being said let's jump into our example where we have a circle with a given diameter of 12 feet now the first thing that i'm going to do is write out the formula for the area of a circle so area equals pi r squared next we can plug in our radius so area equals pi times now we are given the diameter so we need to divide that diameter by 2 to get the radius because remember the radius is half of the diameter 12 divided by 2 gives us a radius of 6 feet let's plug that in and that's going to give us 6 squared now 6 squared that means 6 times 6 not 6 times 2 when we square a number we multiply that number by itself so let's do 6 squared which gives us 6 times 6 which equals 36 so we end up with pi times 36 now one way to write the area of a circle is to write it in terms of pi meaning we can write our number in front of the pi symbol and then put our unit of measure so we can put 36 pi and this is square feet for our unit of measure so that's one way we can write out our area of that circle another option we can use an approximate rounded version of pi like i mentioned earlier we're going to use 3.14 so we can use this to get an approximate area of this circle in decimal form so again we're going to use pi is approximately 3.14 so that squiggly equal sign that's the approximate symbol unlike an equal sign which means an exact value so something to keep in mind when you see that sign let's write out our formula which is area equals pi r squared and then we can plug in so area is approximately i'm going to use the approximate symbol there because again we're using an approximate version of pi so we are going to get an approximate area let's plug in 3.14 and then multiply by our radius which is 6 squared and now we can calculate here let's do 6 squared so 3.14 times 6 squared which equals 36 and now let's multiply so 3.14 times 36 gives us an approximate area of 113 and four hundredths and this is square feet so that is an approximate area of that circle so there you have it there's how you calculate the area of a circle use the formula area equals pi r squared then we can plug in our radius and square it and then go from there as far as how we would like to write out our area we can write it in terms of pi or we can use an approximate version of pi to get an approximate area in decimal form i hope that helped thanks so much for watching until next time peace you