Calculating the area of a sector - GMAT Quantitative

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 is our diameter, our radius is . Thus, our total area is:

We need to go one step further to find the area of sector . Simply multiply the total area by the fractional amount that sector covers. We are told it is of the circle's area, so do the following:

Thus, our answer is .

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 over the total number of degrees in a circle ():

So, we find our answer by multiplying these two parts together:

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 . This means we divide by , and then multiply that fraction by the total area of the circle to give us the area of the sector:

Assume Statement 1 alone. Since the circumference of the circle is not given, it cannot be determined what part of the circle is, and therefore, the central angle of the sector cannot be determined. Also, no information about the circle can be determined. A similar argument can be given for Statement 2 being insufficient.

Now assume both statements are true. Then the length of semicircle is equal to . The circumference is twice this, or . The radius can be calculated as , and the area, . Also, is of the circle, and the area of the sector can now be calculated as .

First we calculate the area of the pizza. The area of a circle is defined as . Since our diameter is 18 inches, our radius is 18/2 = 9 inches. So the total area of the pizza is square inches.

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.

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 is our diameter, our radius is . Thus, our total area is:

We need to go one step further to find the area of sector . Simply multiply the total area by the fractional amount that sector covers. We are told it is of the circle's area, so do the following:

Thus, our answer is .

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 over the total number of degrees in a circle ():

So, we find our answer by multiplying these two parts together:

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 . This means we divide by , and then multiply that fraction by the total area of the circle to give us the area of the sector:

Assume Statement 1 alone. Since the circumference of the circle is not given, it cannot be determined what part of the circle is, and therefore, the central angle of the sector cannot be determined. Also, no information about the circle can be determined. A similar argument can be given for Statement 2 being insufficient.

Now assume both statements are true. Then the length of semicircle is equal to . The circumference is twice this, or . The radius can be calculated as , and the area, . Also, is of the circle, and the area of the sector can now be calculated as .

First we calculate the area of the pizza. The area of a circle is defined as . Since our diameter is 18 inches, our radius is 18/2 = 9 inches. So the total area of the pizza is square inches.

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.

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 is our diameter, our radius is . Thus, our total area is:

We need to go one step further to find the area of sector . Simply multiply the total area by the fractional amount that sector covers. We are told it is of the circle's area, so do the following:

Thus, our answer is .

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 over the total number of degrees in a circle ():

So, we find our answer by multiplying these two parts together:

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 . This means we divide by , and then multiply that fraction by the total area of the circle to give us the area of the sector:

Assume Statement 1 alone. Since the circumference of the circle is not given, it cannot be determined what part of the circle is, and therefore, the central angle of the sector cannot be determined. Also, no information about the circle can be determined. A similar argument can be given for Statement 2 being insufficient.

Now assume both statements are true. Then the length of semicircle is equal to . The circumference is twice this, or . The radius can be calculated as , and the area, . Also, is of the circle, and the area of the sector can now be calculated as .

First we calculate the area of the pizza. The area of a circle is defined as . Since our diameter is 18 inches, our radius is 18/2 = 9 inches. So the total area of the pizza is square inches.

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.

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 is our diameter, our radius is . Thus, our total area is:

We need to go one step further to find the area of sector . Simply multiply the total area by the fractional amount that sector covers. We are told it is of the circle's area, so do the following:

Thus, our answer is .

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 over the total number of degrees in a circle ():

So, we find our answer by multiplying these two parts together:

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 . This means we divide by , and then multiply that fraction by the total area of the circle to give us the area of the sector:

Assume Statement 1 alone. Since the circumference of the circle is not given, it cannot be determined what part of the circle is, and therefore, the central angle of the sector cannot be determined. Also, no information about the circle can be determined. A similar argument can be given for Statement 2 being insufficient.

Now assume both statements are true. Then the length of semicircle is equal to . The circumference is twice this, or . The radius can be calculated as , and the area, . Also, is of the circle, and the area of the sector can now be calculated as .