How to find the angle of a sector - GRE Quantitative Reasoning
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John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
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A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be 
for the smaller piece and 
for the larger one. Thus, we can write the equation:
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
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Quantity A: The angle of a circle's sector having an arc length of 
and a radius of 
.
Quantity B: The angle of a circle's sector having an area of 
and a radius of 
.
Which of the following relations is true?
Quantity A: The angle of a circle's sector having an arc length of
Quantity B: The angle of a circle's sector having an area of
Which of the following relations is true?
For each of these, you need to compute the total measurement applicable to the given data. For Quantity A, this will be the total circumference. For Quantity B, this will be the total area. You will then divide the given sector calculation by this total amount. By multiplying this percentage by 
, you will find the degree measure of each; however, you will merely need to stop at the percentage (since both are percentages of the same number, namely 
).
Quantity A
The total circumference is calculated using the standard equation:
or, for our data: 
Thus, our pertinent percentage is:
Quantity B
For this, the area is computed by the formula:
or, for our data: 
Thus, our percentage is:
Clearly, 
, so A is larger than B.
For each of these, you need to compute the total measurement applicable to the given data. For Quantity A, this will be the total circumference. For Quantity B, this will be the total area. You will then divide the given sector calculation by this total amount. By multiplying this percentage by
Quantity A
The total circumference is calculated using the standard equation:
Thus, our pertinent percentage is:
Quantity B
For this, the area is computed by the formula:
Thus, our percentage is:
Clearly,
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