## anonymous one year ago 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°

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

$\frac{40\pi}{100\pi}=\frac{x}{360}$

7. anonymous

Alright I understand

8. anonymous

k good more?

9. anonymous

Yeah

10. anonymous

k lets knock em ouit