GMAT Math : Calculating the percentage of a sector from an angle

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Example Question #1 : Calculating The Percentage Of A Sector From An Angle

A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?

Possible Answers:

$10\%$

$12.5\%$

$25\%$

$6\%$

Correct answer:

$12.5\%$

Explanation:

The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.

$\frac{x}{100}=\frac{45}{360}$

360x=4500

x=12.5

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Example Question #2 : Calculating The Percentage Of A Sector From An Angle

Consider the Circle :

Circle3

(Figure not drawn to scale.)

Suppose sector BOX covers an area of $\small 27 \pi\:m^2$ . What percentage of the area of the circle does sector BOX cover?

Possible Answers:

$1.2\%$

$12\%$

$0.12\%$

$120\%$

$27\%$

Correct answer:

$12\%$

Explanation:

To find the percentage of the area of the circle that sector BOX covers, divide the area of sector BOX by the total area of the circle:

Area of the circle:

$\small A=\pi r^2=\pi (15\:m)^2=225 \pi\:m^2$

Percentage:

$\frac{27 \pi \:m^2}{225 \pi \:m^2}=\frac{27}{225}=\frac{3}{25} =0.12$

To go from a decimal to a percent, multiply by 100 . This gets us to $12\%$ , the correct answer.

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Example Question #3 : Calculating The Percentage Of A Sector From An Angle

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?

Possible Answers:

$11.1\%$

$29.2\%$

$22.2\%$

$44.4\%$

$80.8\%$

Correct answer:

$22.2\%$

Explanation:

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:

$\frac{80}{360}=\frac{8}{36}=\frac{2}{9}=.2\bar{2}$

From here multiply by 100 to get the percentage.

$0.22\cdot 100=22.2\%$

So the first slice represents about 22.2% of the total cake!

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Example Question #4 : Calculating The Percentage Of A Sector From An Angle

If a sector has an angle of $18^{\circ}$ , what percentage of the circle's area is covered by the sector?

Possible Answers:

$9\%$

$18\%$

$5\%$

$36\%$

$10\%$

Correct answer:

$5\%$

Explanation:

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, $360^{\circ}$ . The given sector has an angle of $18^{\circ}$ , so whatever percent this is of $360^{\circ}$ will tell us what percent of the circle's area is covered by the sector:

$\frac{18^{\circ}}{360^{\circ}}=\frac{1}{20}=0.05=5\%$

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Example Question #5 : Calculating The Percentage Of A Sector From An Angle

What percentage of a circle is a sector if the angle of the sector is $27^{\circ}$ ?

Possible Answers:

$7.5\%$

$10\%$

$5\%$

$27\%$

$13.5\%$

Correct answer:

$7.5\%$

Explanation:

The full measure of a circle is $360^{\circ}$ , so any sector will cover whatever fraction of the circle that its angle is of $360^{\circ}$ . We are given a sector with an angle of $27^{\circ}$ , so this sector will cover a percentage of the circle equal to whatever fraction $27^{\circ}$ is of $360^{\circ}$ . This gives us:

$\frac{27^{\circ}}{360^{\circ}}=\frac{3}{40}=0.075=7.5\%$

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Example Question #6 : Calculating The Percentage Of A Sector From An Angle

What percentage of a circle's total area is covered by a sector with an angle of $54^{\circ}$ ?

Possible Answers:

$27\%$

$15\%$

$54\%$

$10\%$

$12.5\%$

Correct answer:

$15\%$

Explanation:

The full measure of a circle is $360^{\circ}$ , so any sector will cover whatever fraction of the circle that its angle is of $360^{\circ}$ . We are given a sector with an angle of $54^{\circ}$ , so this sector will cover a percentage of the circle equal to whatever fraction $54^{\circ}$ is of $360^{\circ}$ . This gives us:

$\frac{54^{\circ}}{360^{\circ}}=\frac{3}{20}=0.15=15\%$

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GMAT Math : Calculating the percentage of a sector from an angle

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Example Questions

Example Question #1 : Calculating The Percentage Of A Sector From An Angle

Example Question #2 : Calculating The Percentage Of A Sector From An Angle

Example Question #3 : Calculating The Percentage Of A Sector From An Angle

Example Question #4 : Calculating The Percentage Of A Sector From An Angle

Example Question #5 : Calculating The Percentage Of A Sector From An Angle

Example Question #6 : Calculating The Percentage Of A Sector From An Angle

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