Question

In a circle of radius 10 cm, a sector has an area of 40pi sq. cm. What is the degree measure of the arc of the sector?

a) 72°
b) 144°
c) 180°

Answer 1

total area of the circle is \(\pi r^2\) which in your case is \(\pi\times 10^2=100\pi\)

Answer 2

the sector has area \(40\pi\) and \(\frac{40\pi}{100\pi}=\frac{4}{10}\) in other words the area of the sector is four tenths of the total area

Answer 3

the entire circle has \(360^\circ\)
to find your portion, compute
\[\frac{4}{10}\times 360\] or
\[.4\times 360\]

Answer 4

It's 144. But why not multiply it by 180 though?

Answer 5

this is a different knd of problem than the last one
we are not converting from degrees to radians or anything
just computing a ratio

Answer 6

\[\frac{40\pi}{100\pi}=\frac{x}{360}\]

Answer 7

Alright I understand

Answer 8

k good
more?

Answer 9

Yeah

Answer 10

k lets knock em ouit