A circle has a radius of 8 inches. Find the area of a sector of the circle if the sector has an arc that measures 45°.

Question

hero · Answer

calistar, have you considered applying the general formula I gave you?

anonymous · Answer

srry i still dnt understand=/

hero · Answer

What is it that you don't understand?

anonymous · Answer

correct me if im wrong, is it 8pi squared inches

hero · Answer

How did you get that?

hero · Answer

Show me your work.

anonymous · Answer

it was a educational guess

2bornot2b · Answer

$$\frac{[(\pi\times8^2)(8\times \pi/2)]}{(2\pi\times8)}$$

hero · Answer

Calistar, I'm only going to show you this once. If you don't get it, tell me what it is that you don't get. I'm going to explain it to you the best way that I can.

hero · Answer

In general, you are given a circle, a radius, and the angle, θ, that cuts across a given arc: 
|dw:1327093977310:dw|

and you are essentially asked to find the length of arc AC.

The general formula to find the length of arc AC is given by the following: 

$$\frac{\theta}{360°} = \frac{x}{2 \pi r}$$, x = length of arc AC. Solving for x gives you the length of arc AC. 

In this particular case, you are given θ = 45°, and r = 8, and asked to find the arc length, x, of the portion of the circle that θ = 45° cuts across. It would look something like this: 

|dw:1327094386599:dw|

Since we are given some of the components of the general formula such as 
θ = 45° and r = 8, we can substitute that into the formula and solve for x. Here's the setup: 

$$\frac{45}{360} = \frac{x}{2 \pi 8}$$. All you need to do at this point is to cross multiply and solve for x. Do you believe you can do this?