GMAT Math : Calculating the area of a sector
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Example Questions
Example Question #1 : Calculating The Area Of A Sector
A teacher buys a supersized pizza for his after-school club. The super-pizza has a diameter of 18 inches. If the teacher is able to perfectly cut from the center a 36 degree sector for himself, what is the area of his slice of pizza, rounded to the nearest square inch?
26
25
28
24
27
25
First we calculate the area of the pizza. The area of a circle is defined as 
Since the sector of the pie he cut for himself is 36 degrees, we can set up a ratio to find how much of the pizza he cut for himself. Let x be the area of the pizza he cut for himself. Then we know,
Solving for x, we get x=25.45 square inches, which rounds down to 25.
Example Question #2 : Calculating The Area Of A Sector
In the figure shown below, line segment 
Find the area of sector 
To find the area of a sector, we need to know the total area as well as the fractional amount of the sector at which we are looking.
In this case, we find the total area by using the following equation:
Because line segment 
We need to go one step further to find the area of sector 
Thus, our answer is 
Example Question #3 : Calculating The Area Of A Sector
Consider the Circle 
(Figure not drawn to scale.)
If angle 
To find the area of a sector, simply multiply the total area of the circle by the fraction of the part you are looking at.
In this case, our area will come from the following:
To find the fractional part of the circle we care about, take the number of degrees in 
So, we find our answer by multiplying these two parts together:
Example Question #1 : Calculating The Area Of A Sector
If a circle has an area of 
The area of a sector with a certain angle will be whatever fraction of the total circle's area the angle of the sector is of 
Example Question #5 : Calculating The Area Of A Sector
The circle in the above diagram has center 
Statement 1: Arc 
Statement 2: Arc 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. Since the circumference of the circle is not given, it cannot be determined what part of the circle 
Now assume both statements are true. Then the length of semicircle 
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