<p>I'm stuck on this one, I thought I knew how to solve it, but I keep getting weird wrong answers.</p>
<p>AB is the arc of a circle with center O. If the length of arc AB is 7pi what is the area of region OAB to the nearest integer?</p>
<p>Thanks</p>
<p>is this all the given information? or did we get a diagram or something?</p>
<p>Oh whoops, forgot a bit of crucial info… The angle of the circle of arc AB is 55 degrees</p>
<p>I might be wrong, but anyways. So first you need to find the length of the radius so that you can use the following formula to find the area of the sector: pi(r)^2 x (measure of angle/360). To find the radius, you must first set up a proportion: 7pi/55 = x/360 so that you can find the circumference of the whole circle. X (the circumference of the entire circle ) = 143.9420
From here, inversely use the circumference formula (C=2pi x radius)) to find the radius. So you would set it up as 143.9420=2pi(radius). Radius equals 22.9090
So now back to the sector formula, which was pi(r)^2 x (measure of angle/360). Just fill up the formula: pi(22.9090)^2 x (55/360). And now you get a grand, and hopefully correct, answer of 251.8966, which you round to 252.</p>
<p>not sure if this is right, but…</p>
<p>x = multiplication
r = radius</p>
<p>2(pi)(r) x (55/360) = 7(pi)
Solve r,
r = 252/11 or 22.9</p>
<p>(pi)(r^2) x (55/360) = area OAB.
(pi)(22.9^2) x (55/360) = …
Solve this…</p>
<p>area OAB = 251.899</p>
<p>round to nearest integer… </p>
<p>OAB = 252 units^2</p>
<p>Got the same answer^^
Basically you should’ve known that the area of a sector is (x/360) * (pi)(r^2) and the arc of a sector is (x/360) * (2)(pi)(r).</p>
<p>Solve for the radius and plug it into the area of a sector formula.</p>