The radius of a circle is 6 inches. What is the area of a sector bounded by a 90° arc?

[1] Let's make the problem easier to start. Imagine that they had said to find the area of a sector bounded by a 360* arc (the whole circle). Could we have found the area then? 

Sure we could! We know that A = pi*r^2, so that would just be:

A = pi*(6)^2 = 36*pi sq. miles.

Easy. But of course, we weren't so lucky... they want 135*... drat!

[2] Well, let's get a little closer, could we find the area if the angle was 180*? Sure! That's just half the circle. After all:

180*/360* = 1/2.

We know the whole circle is 36*pi sq. miles. So, the area bounded by a 180* arc would just be half of this: 18*pi sq. miles. 

"But that's not the question," you scream!! Alright, alright, calm down... let's bring it all together.

[3] We know the area of the whole circle [1]. We also know that if we can figure out the fraction of the circle the problem is easy [2]. So, what fraction of a circle would match an arc of 135*?

Well, we can see that

135*/360* = 0.375    or    3/8

So the area is just 0.375 of the whole circle:

0.375* 36*pi sq. miles = 13.5*pi sq. miles

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step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )