11-3 Finding Area of Circles and Sectors

The squared number 5 is 6082.1 meters squared and number 6 is 380.1 inches squared. Questions anybody. Easy easy. Okay. Okay, on the second page, this is where we're going to work backwards. They give you the area and you were to find either the readiest or the diameter. So the area of the circle is a 153.9 and you are finding the diameter. So take your formula, area equals R squared, plug in everything you know. I know what the area is. It's a 153.9. And that's all they tell me. So we're going to solve for R because if I can find the R I can then find the diameter. So we're going to divide. Cancels. Divide by pi. One 53 divided. .9 divided by pi. It's going to give you about 48.99. And that equals R squared. I don't want R squared. I will just R, so what do I do? Take the square root. Now you rounded this up to just 49 that'll work too. So take the square root, so R is going to be equal to 6.99 or approximately 7, but we don't want R we want the diameter, so we know that the diameter is twice that, so if we take our R and we multiply it by two, that's going to give us the diameter, which is equal to 14. 

Okay, take a look at the next one number 8. I'm going to give you a minute to do number 8 on your own. Okay, so number 8, we are finding the diameter of the circle and it has an area of 490.9, so area equals R squared. I know the area is 490.9 equals pi R squared, divide both sides by pi. This cancels out, at least maybe with R squared. 490.9 divided by pi is going to give you one 56 point three. I don't want R squared, so I'm going to have to type my one 56.3, and take the square root of it, and that gives me R so I'm going to find my square root, that's going to be about 12.5, but I'm not looking for R I'm looking for the diameter. So let me use your diameter is double that, which would be 25. 25? Excellent. Okay, let's do number 9. Okay, let's check number 9. The area of the circle is 907.9 square inches on the right is this time we're only looking for the radius. So the area is 907.9 and then equals pi R squared, so divide by pi. Divide by and you get 288.99 equals R squared. If you take the square root of that, that gives you 17 for approximately 17 is equal to R do I need to double it? No, because I'm only looking for the radius. So there's my answer out there. All right, number ten, not done number ten yet, go ahead and do that real quick. 

Okay, let's check number ten. We have an area of 63.6. Equals R squared, so we're going to divide by. Divide by, and you get 20.44 equals the radius squared, so we're going to take the square root of that. So R is equal to 4.5. If I get 4.5, excellent. Okay, turn to the next page. This is the new information. Everything else has been reviewed so far. All right, up here where you have a little bit of empty space. I want you to write this proportion. We did this earlier in the year with length. Now we're going to do it with area. It's the same thing. We're going to do the angle degree over the circle degree, and it equals the area of your sector over the area of the circle. That is the proportion that we will set up to solve the area of a piece of a circle's sector is a piece of it suck a piece of ha. Okay, so looking at number one. You know we're going to sit up at proportion. We need our angle degree, which would be 45. Over the whole circle degree, which we know is 360°. The area of the sector is what we're looking for that you're shaded area that's X, and the area the circle is your formula, pa times, the radius, which is three squared. Do we remember how to solve a portion? Yes, cross multiply and divide. 

So you can do 45 times three squared divided by 360. You can do that all in one problem in your calculator. And find out what the area of the sector is. And you should get. 3.5 feet squared, there's a point there. Okay, number two, so you have to be very exact same way. Area see the angle of the area of the circle would be a 100°. The whole circle is 360°, area of your sector we do not know that your shaded part, let's X, area of the whole circle is par time, your radius, ten squared, and then we cross multiply and divide. Okay, questions. I want to invite you to do number three. I'll give you a minute to okay, let's take a look at number three. Now, remember, we're looking for the shaded sector. That means I want to know the area of all of this shaded area, but not that little B sliver. So if the sliver is 20°, then in order to find the degree of everything else, we would take 360 minus the 20 and that would give us 340 for our angle over 360 for the whole circle. X is the area of the big sector and part times your righteous squared is the area of your whole circle. 

Rawls multiply and divide. And you should have gotten a 145.4 meters squared. Questions on that one? Did everybody get it? Did you do it backwards? Backwards. Be careful there. We're looking for The Shining. You get used to only looking for the little piece and you don't think about what you're doing, but it did specify shaded sector. So be careful there. Okay. Number four, 5 and 6. Go ahead and work out all three of those and then we'll come back and check them. Okay, let's check your age or see what we have. Number four 52.4. 5. 282.7 feet that's not feed that is meters squared. And number 6 43.2 centimeters squared. Questions on any of that.