Calculating the percentage of a sector from an angle - GMAT Quantitative
Card 1 of 48
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
Tap to reveal answer
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
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Consider the Circle 
:
(Figure not drawn to scale.)
Suppose sector 
covers an area of 
. What percentage of the area of the circle does sector 
cover?
Consider the Circle
(Figure not drawn to scale.)
Suppose sector
Tap to reveal answer
To find the percentage of the area of the circle that sector 
covers, divide the area of sector 
by the total area of the circle:
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by 
. This gets us to 
, the correct answer.
To find the percentage of the area of the circle that sector
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by
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If a sector has an angle of 
, what percentage of the circle's area is covered by the sector?
If a sector has an angle of
Tap to reveal answer
The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle, 
. The given sector has an angle of 
, so whatever percent this is of 
will tell us what percent of the circle's area is covered by the sector:
The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle,
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Circle T represents a round birthday cake. If the first slice will have a central angle of 
degrees, what percentage of the total cake is in the first slice?
Circle T represents a round birthday cake. If the first slice will have a central angle of
Tap to reveal answer
In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:
From here multiply by 100 to get the percentage.
So the first slice represents about 22.2% of the total cake!
In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:
From here multiply by 100 to get the percentage.
So the first slice represents about 22.2% of the total cake!
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What percentage of a circle is a sector if the angle of the sector is 
?
What percentage of a circle is a sector if the angle of the sector is
Tap to reveal answer
The full measure of a circle is 
, so any sector will cover whatever fraction of the circle that its angle is of 
. We are given a sector with an angle of 
, so this sector will cover a percentage of the circle equal to whatever fraction 
is of 
. This gives us:
The full measure of a circle is
← Didn't Know|Knew It →
What percentage of a circle's total area is covered by a sector with an angle of 
?
What percentage of a circle's total area is covered by a sector with an angle of
Tap to reveal answer
The full measure of a circle is 
, so any sector will cover whatever fraction of the circle that its angle is of 
. We are given a sector with an angle of 
, so this sector will cover a percentage of the circle equal to whatever fraction 
is of 
. This gives us:
The full measure of a circle is
← Didn't Know|Knew It →
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
Tap to reveal answer
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
← Didn't Know|Knew It →
Consider the Circle :
(Figure not drawn to scale.)
Suppose sector covers an area of . What percentage of the area of the circle does sector cover?
Consider the Circle
(Figure not drawn to scale.)
Suppose sector
Tap to reveal answer
To find the percentage of the area of the circle that sector covers, divide the area of sector by the total area of the circle:
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by . This gets us to , the correct answer.
To find the percentage of the area of the circle that sector
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by
← Didn't Know|Knew It →
If a sector has an angle of , what percentage of the circle's area is covered by the sector?
If a sector has an angle of
Tap to reveal answer
The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle, . The given sector has an angle of , so whatever percent this is of will tell us what percent of the circle's area is covered by the sector:
The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle,
← Didn't Know|Knew It →
Circle T represents a round birthday cake. If the first slice will have a central angle of degrees, what percentage of the total cake is in the first slice?
Circle T represents a round birthday cake. If the first slice will have a central angle of
Tap to reveal answer
In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:
From here multiply by 100 to get the percentage.
So the first slice represents about 22.2% of the total cake!
In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:
From here multiply by 100 to get the percentage.
So the first slice represents about 22.2% of the total cake!
← Didn't Know|Knew It →
What percentage of a circle is a sector if the angle of the sector is ?
What percentage of a circle is a sector if the angle of the sector is
Tap to reveal answer
The full measure of a circle is , so any sector will cover whatever fraction of the circle that its angle is of . We are given a sector with an angle of , so this sector will cover a percentage of the circle equal to whatever fraction is of . This gives us:
The full measure of a circle is
← Didn't Know|Knew It →
What percentage of a circle's total area is covered by a sector with an angle of ?
What percentage of a circle's total area is covered by a sector with an angle of
Tap to reveal answer
The full measure of a circle is , so any sector will cover whatever fraction of the circle that its angle is of . We are given a sector with an angle of , so this sector will cover a percentage of the circle equal to whatever fraction is of . This gives us:
The full measure of a circle is
← Didn't Know|Knew It →
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
Tap to reveal answer
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
← Didn't Know|Knew It →
Consider the Circle :
(Figure not drawn to scale.)
Suppose sector covers an area of . What percentage of the area of the circle does sector cover?
Consider the Circle
(Figure not drawn to scale.)
Suppose sector
Tap to reveal answer
To find the percentage of the area of the circle that sector covers, divide the area of sector by the total area of the circle:
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by . This gets us to , the correct answer.
To find the percentage of the area of the circle that sector
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by
← Didn't Know|Knew It →
If a sector has an angle of , what percentage of the circle's area is covered by the sector?
If a sector has an angle of
Tap to reveal answer
The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle, . The given sector has an angle of , so whatever percent this is of will tell us what percent of the circle's area is covered by the sector:
The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle,
← Didn't Know|Knew It →
Circle T represents a round birthday cake. If the first slice will have a central angle of degrees, what percentage of the total cake is in the first slice?
Circle T represents a round birthday cake. If the first slice will have a central angle of
Tap to reveal answer
In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:
From here multiply by 100 to get the percentage.
So the first slice represents about 22.2% of the total cake!
In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:
From here multiply by 100 to get the percentage.
So the first slice represents about 22.2% of the total cake!
← Didn't Know|Knew It →
What percentage of a circle is a sector if the angle of the sector is ?
What percentage of a circle is a sector if the angle of the sector is
Tap to reveal answer
The full measure of a circle is , so any sector will cover whatever fraction of the circle that its angle is of . We are given a sector with an angle of , so this sector will cover a percentage of the circle equal to whatever fraction is of . This gives us:
The full measure of a circle is
← Didn't Know|Knew It →
What percentage of a circle's total area is covered by a sector with an angle of ?
What percentage of a circle's total area is covered by a sector with an angle of
Tap to reveal answer
The full measure of a circle is , so any sector will cover whatever fraction of the circle that its angle is of . We are given a sector with an angle of , so this sector will cover a percentage of the circle equal to whatever fraction is of . This gives us:
The full measure of a circle is
← Didn't Know|Knew It →
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
Tap to reveal answer
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
← Didn't Know|Knew It →
Consider the Circle :
(Figure not drawn to scale.)
Suppose sector covers an area of . What percentage of the area of the circle does sector cover?
Consider the Circle
(Figure not drawn to scale.)
Suppose sector
Tap to reveal answer
To find the percentage of the area of the circle that sector covers, divide the area of sector by the total area of the circle:
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by . This gets us to , the correct answer.
To find the percentage of the area of the circle that sector
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by
← Didn't Know|Knew It →