area of an annulus

[flipflopchic]

im trying to figure out the measure of angle abc. The angle is in an annulus and in the outide ring of the annulus it is shaded inside the angle. I know that the shaded area is 10 pi centimeters squared. R=10, r=8.
I know you have to take pi R squared - pi r squared so it would be 100 pi minus 64 pi. That gives me 36 pi. After this i am stuck. i have to keep my answers in the pi form

 

[galactus]

The area of the entire annulus would be \(\displaystyle 100{\pi}-64{\pi}=36{\pi}\approx{113.10}\)

Is the majority of your annulus shaded?. Because \(\displaystyle 10{\pi}^{2}\approx{98.7}\)

That is a large chunk of the entire thing.

You can use the area of a circular sector formula, \(\displaystyle \frac{1}{2}{\theta}r^{2}\)

\(\displaystyle \frac{1}{2}{\theta}(10)^{2}-\frac{1}{2}{\theta}(8)^{2}=10{\pi}^{2}\)

Solve for \(\displaystyle {\theta}\)

It'll be in radians, so if your need degrees you will have to convert.

 

[flipflopchic]

no only the part that is cut of by the angle is shaded. the majority is unshaded

 

[galactus]

But I can't see that. I am guessing. The method outlined should work nonetheless.

 

[flipflopchic]

ok so where did you get those numbers for the equation? thats where i get lost

 

[galactus]

Where did I get the numbers?. You gave them to me.

 

[flipflopchic]

wow im sorry that was a stupid question.

how do you go from radians to degrees?

 

[tkhunny]

how do you go from radians to degrees?

\(\displaystyle \pi = 180^{\circ}\), but why do you want to know?

"i have to keep my answers in the pi form"

 

[galactus]

With all due respect, if you're that lost you might see your instructor. To change from radians to degrees just multiply by

\(\displaystyle \frac{180}{\pi}\)

But, as tkh pointed out, since you need your answers in 'Pi form', radians are what you want....not degrees.

 

[flipflopchic]

ok thanks