in this video we're going to talk about how to calculate the area and the circumference of a circle but first let's talk about the radius and the diameter of a circle my draw is not perfect but we're going to make the best of that so here is the center of the circle it's a point right at the middle of the circle now the distance between the center of the circle and any point on the circle that is known as the radius of the circle the diameter is twice the value of the radius so let's say this is the center of the circle the diameter starts from one end of the circle it passes through the center and connects to the other end of the circle so as you can see visually it's twice as long as the radius of the circle so we can say that d is equal to 2r now the next thing you need to be familiar with is the area and the circumference of a circle the area is basically the area of the shader region to calculate the area of a circle you could use this formula it's pi times r squared now the circumference is basically the distance around the edge of the circle so this is the circumference and to calculate the circumference it's equal to 2 pi times r now pi is equal to three point one four one five nine two six five four and there are more other numbers you know that go on after that but typically when solving these problems in school you'll be using approximate value of pi which is usually 3.14 so now let's work on some problems let's start with this one number one calculate the area and circumference of the circle shown below use pi equal 3.14 so let's start with the area the area is equal to pi r squared the radius we can clearly see that the radius of this circle is 5 feet it's the distance between the center and the point on a circle so we have pi times five feet squared five squared is five times five which is 25 and feet times feet gives you square feet so the units of area is always square units square inches square feet square yards and so forth now the exact answer for the area of the circle is 25 pi square feet we're going to get an approximation using this value so let's replace pi with 3.14 so the answer for this problem the area is approximately 78.5 square feet so that's how you can calculate the area of a circle if you're given the radius of that circle now let's move on to the second part of the problem let's calculate the circumference of the circle so we're going to use the formula c is equal to two pi r let's get the exact value first so let's replace the radius with five feet 2 pi times 5 is 10 pi so the exact answer is 10 pi feet so notice that the unit for circumference is in feet which is the same as unit for radius but the unifi area is in square feet now let's replace pi with 3.14 so this will give us an approximate answer 10 times 3.14 is going to be 31.4 so the circumference of this particular circle is 31.4 feet so if you were to start here let's say on a track and you would let's say you were to walk around in this circle you would travel a distance of 31.4 feet so that's what that means given that the radius of the circle is 5 feet now let's work on a similar problem at this time we're given the diameter of the circle the diameter is 14 inches how can we use the diameter to calculate the area and the circumference of the circle well the first thing we need to do is we need to find the radius remember the diameter is twice the length of the radius so if we divide both sides of this equation by 2 we'll get that the radius is half of the diameter half of 14 or 14 divided by 2 is 7. so the radius of this circle is 7 inches so now that we know the radius of the circle we can calculate the area and the circumference so let's start with the area we know the area is pi r squared so let's replace r with 7 inches 7 squared or 7 times 7 is 49 so we get that the area is 49 pi square inches so this right here is the exact answer but now let's replace pi with 3.14 49 times 3.14 that's 153.86 but we're going to do is we're going to round our answer to 154 square inches so that's the area of the circle in this problem now let's calculate the circumference the circumference is 2 pi r let's replace r with 7 inches so we have 2 pi times 7 so we get an exact answer of 14 pi inches now let's get our approximate answer by replacing pi with 3.14 14 times 3.14 that's 43.96 but since we use 3.14 for pi i like to round my answer to three significant figures so i'm going to round it to 44.0 inches so that's the approximate value for the circumference of the circle number two the area of a circle is 28.5 square inches what is the radius of the circle so we're going to use 3.14 for pi we're going to round our answer to the nearest hundredth place so let's start with this formula area is equal to pi r squared so we're going to replace the area with 28.5 square inches and we're going to replace pi with 3.14 and we're going to solve for r in order to do that we need to divide both sides by 3.14 so we get 28.5 divided by 3.14 and that works out to be nine point zero seven six four three three with some other numbers but this should be good enough so that is equal to r squared to get r we need to take the square root of both sides so the square root of 9.07643 we could round the answer so let's use our approximate symbol so we're going to round it to 3.01 so that's the nearest hundredth so this is the radius of the circle that's how we could find it if we're given the area of the circle and by the way let's not forget the unit for radius the unit for area is square inches so the unit for the radius of this circle is going to be just inches the radius diameter circumference they have units like inches feet yards things like that area is always square units so just keep that in mind but these two they must match number three the circumference of a circle is 14.5 feet what is the diameter of the circle so the formula that we need to use is circumference is equal to 2 pi r now what we need to do here is we need to use the circumference to calculate the radius of the circle once we have the radius of the circle we could then find the diameter of the circle because we know that the diameter is twice the value of the radius of the circle so let's calculate r first let's replace c with 14.5 feet unless you place pi with 3.14 2 times 3.14 that's 6.28 so to get r by itself we need to divide both sides by 6.28 14.5 divided by 6.28 we get 2.3089 and we're going to round it to the nearest tenth i mean to the nearest hundredth so that's going to be 2.31 now let's put the units so the unit for circumference is in feet that's going to be the same for the unit of radius so now that we have the radius we can find the diameter the diameter is simply 2r is twice the value of r so it's going to be 2 times 2.31 2 times 2 is 4 2 times 31 is 62. so the diameter of this circle is going to be approximately 4.62 feet number four the circumference of a circle is 18 pi meters what is the area of the circle go ahead and try that problem so let's begin with this equation c is equal to 2 pi r so that's our circumference equation and we also know that the area is pi r squared so those are the two equations that we have so we're given the circumference and we need to find in the area what we need to do is we need to use the circumference to get the radius once we have the radius we could plug it into the second equation to get the area so let's go ahead and do that so we're going to replace the circumference with what it equals 18 pi meters now we're going to solve for r to get r by itself we need to divide both sides by 2 pi on the right side 2 pi will cancel on the left side pi will cancel and we're going to have 18 divided by two which is nine so this is the radius of the circle it's nine and since the unit for circumference is in meters the radius is going to be in meters as well so this is an exact answer so now let's use that to calculate the area so let's replace r with 9 meters 9 squared is 81. so the exact answer for the area will be 81 pi square meters now let's get our approximate answer let's replace pi with 3.14 so 81 times 3.14 that's 254.34 so we're going to round that to the nearest whole number which will be 254. so that's the approximate area of the circle it's 254 square meters that's the answer number five the area of a circle is a hundred square yards what is the circumference of the circle so let's write the two equations that we're going to use a is equal to pi r squared and c is equal to 2 pi r so this problem is basically the reverse of the previous problem we're given the area we're going to use that to calculate r once we have r we're going to plug it into this equation to get the circumference so let's replace a with 100 square yards and let's plug in pi as 3.14 so to get r by itself what we're going to do is we're going to divide both sides by 3.14 100 divided by 3.14 and that is 31.847133 and that's square yards so to get r we need to take the square root of both sides so the square root of 31.847133 that's five point six four three three three and the square root of yards squared is just yards so this is the approximate value for the radius so now we're going to take that answer and plug it in to the circumference equation so we have c is equal to 2 pi but we're going to use 3.14 for pi and then we're going to replace r with 5.6433 yards so you should get 35.440 but we're going to round it to the nearest tenth so we're going to say that the circumference is approximately 35.4 and the unit is going to be yards so that's how you can calculate the circumference if you know the area of the circle and that's basically it for this video thanks for watching