Unit 11 volume and surface area homework 3 answer key

Video Transcript

Number two. We have a circle And we know our central angle is 119. And we're trying to find the area of our sector And then we know our radius is 20. So to find the area of your sector, that's the measure of your angle divided by 360 times pi r squared. And just type that entry calculator round to the nearest 10th. We get 415 0.39. Eat squared number four. We have our circle here. You know this is 87 And we know our radius is 14.2 and we're trying to find the area of this sector here But we still have to use our sector formula but we're not going to plug in 87. We're actually going to plug in 273 Because our whole circle is (360 and 316 -87 is 300 or 273 And the new times by pi R squared. Again, type that in your calculator, we get 480 .38 m squared And then six have our circle And we know our radius is 2.8 and we know that this measure here is 3 11 and we're trying to find the measure or the area of that sector and again we're not going to plug in 3 11. We have to find that ankle measure. So 3 60 minus 3 11. We get 49 and then times by pi R squared And when you do that, we get 3.35 inches squared. And then number eight gonna have our glass looking. We know that this angle here is 108 and we know our radius is 5.3 and we're trying to find the shaded region here. And in order to do that, we can still use area of our sector but we have to find that angle measure. Well we have our diameters here that forms a line, so 180 -108. We get 72. And since these are vertical angles, we also know that this angle is 72. And since we have to find both areas, add up 72 and 72 and we get 1 44 And then plug it in our calculator to simplify, we get 35 0.30 kilometers squared. And then our last one here we have a diameter drawn in. We know that these two arcs are concurrent. We know that this measure here is 73 and our diameter was 26. So half of that we get 13 for our radius so area equals times pi r squared. But we have to find the area of the red part here, which means we have to find the measure of our angle. Well, since Um we know that these two are concurrent. We know that the single over here is 73 And if we do 180 -73 minus 73. So again, we have our diameter here, if this angle 73, we know that this angle is 73. So this angle here is 34 Because we did 180 -73 -73 and this is our diamond. So we know that our angle here is 1 80 so 34 plus 1 80 we get to 14 Plug that in our calculator, we get 315.61 m squared.