GRE Math : How to find the percentage of a sector from an angle

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Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A circle of radius , for an angle , has an arc length of $3\pi$ . What is the angle ?

Gre circle 2

Possible Answers:

$216^{\circ}$

$43.2^{\circ}$

$144^{\circ}$

$54^{\circ}$

$108^{\circ}$

Correct answer:

$108^{\circ}$

Explanation:

The formula for an arc length, , of a circle of a given radius, , and a given angle, is:

$l=2\pi r(\frac{x}{360})$

Note that $2\pi r$ is the circumference of the circle.

Conversely, for a known arc length and unknown angle, this equation can be rewritten as follows:

$x=360(\frac{l}{2\pi r})$

Plugging in the given values, it is therefore possible to find the missing angle:

$x=360(\frac{3\pi }{2\pi(5 )})=108^{\circ}$

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Example Question #1 : How To Find The Percentage Of A Sector From An Angle

Find the radius of the given circle:

Gre circle 3

Possible Answers:

The answer cannot be determined from the information given.

$36\pi$

Correct answer:

Explanation:

To solve this problem, realize that an inscribed angle (an angle formed by two chords) is equal to twice the central angle formed by connecting the origin to the inscribed angle's endpoints:

Gre circle 3 solution

Now, the formula for an arc length, , of a circle of a given radius, , and a given angle, is:

$l=2\pi r(\frac{x}{360})$

Since the radius is the unknown, this equation can be rewritten as:

$r=(\frac{360}{x})(\frac{l}{2\pi })$

Plugging in our values, we find:

$r=\frac{360}{60}\frac{6\pi}{2\pi}=18$

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Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A given pizza with a -inch diameter has 1450 calories. A baker cuts the pizza using a $25^{\circ}$ angle for each piece. If Susan eats five such pieces, how many calories does she consume? Round to the nearest calorie.

Possible Answers:

125

487

503

375

Correct answer:

503

Explanation:

To solve this, notice that one piece of pizza comprises $\frac{25}{360}$ of the total pie or (reducing) $\frac{5}{72}$ of a pie. Now, if Susan buys five slices, she gets:

$\frac{5}{72} \cdot 5 = \frac{25}{72}$ of the pie. If the complete pie contains 1450 calories, she will then eat the following amount of calories:

$\frac{25}{72} \cdot 1450 = 503.47$

Rounding, this is 503 calories.

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GRE Math : How to find the percentage of a sector from an angle

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

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