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ISEE Upper Level Math : How to find the length of a radius

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Example Questions

Example Question #1 : How To Find The Length Of A Radius

What is the radius of a circle with circumference equal to $36\pi$ ?

Possible Answers:

r=9

r=3

r=18

r=6

Correct answer:

r=18

Explanation:

The circumference of a circle can be found using the following equation:

$C=d\pi=2r\pi$

$36\pi=2r\pi$

$\frac{36\pi}{\pi}=\frac{2r\pi}{\pi}$

36=2r

$\frac{36}{2}=\frac{2r}{2}$

18=r

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Example Question #1 : Radius

What is the value of the radius of a circle if the area is equal to $18\pi$ ?

Possible Answers:

$2\sqrt{3}$

$3\sqrt{2}$

Correct answer:

$3\sqrt{2}$

Explanation:

The equation for finding the area of a circle is $\pi r^{2}$ .

Therefore, the equation for finding the value of the radius in the circle with an area of $18\pi$ is:

$\pi r^{2}=18\pi$

$r^{2}=18$

$r=\sqrt{18}=\sqrt{9\cdot 2}=3\sqrt{2}$

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Example Question #2 : Radius

What is the radius of a circle with a circumference of $24\pi$ ?

Possible Answers:

r=10

r=12

r=9

r=24

r=8

Correct answer:

r=12

Explanation:

The circumference of a circle can be found using the following equation:

$C=2r\pi$

We plug in the circumference given, $24\pi$ into and use algebraic operations to solve for .

$24\pi=2r\pi$

$\frac{24\pi }{\pi }=\frac{2r\pi }{\pi }$

24=2r

$\frac{24}{2}=\frac{2r}{2}$

r=12

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Example Question #2 : How To Find The Length Of A Radius

Inscribed angle

Refer to the above diagram. $\overarc {ACB}$ has length $60 \pi$ . Give the radius of the circle.

Possible Answers:

100

Correct answer:

Explanation:

Inscribed $\angle ACB$ , which measures $72 ^{\circ }$ , intercepts a minor arc with twice its measure. That arc is $\overarc {AB}$ , which consequently has measure

$72 ^{\circ } \times 2 = 144 ^{\circ }$ .

The corresponding major arc, $\overarc {ACB}$ , has as its measure

$360 ^{\circ } - 144 ^{\circ } = 216 ^{\circ }$ , and is

$\frac{ 216 }{360 } = \frac{ 216 \div 72 }{360 \div 72 } = \frac{3}{5}$

of the circle.

If we let be the circumference and be the radius, then $\overarc {ACB}$ has length

$\frac{3}{5} C = \frac{3}{5} \cdot 2 \pi r = \frac{6 \pi}{5} r$ .

This is equal to $60 \pi$ , so we can solve for in the equation

$\frac{6}{5} \pi r = 60 \pi$

$\frac{5}{6 \pi } \cdot \frac{6 \pi }{5} r = \frac{5}{6 \pi } \cdot 60 \pi$

r = 50

The radius of the circle is 50.

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Example Question #3 : How To Find The Length Of A Radius

A circle has a circumference of $768\pi m$ . What is the radius of the circle?

Possible Answers:

384 m^2

384 m

125 m

Not enough information to determine.

Correct answer:

384 m

Explanation:

A circle has a circumference of $768\pi m$ . What is the radius of the circle?

Begin with the formula for circumference of a circle:

$Circumference=2\pi r$

Now, plug in our known and work backwards:

$768\pi m=2\pi r$

Divide both sides by two pi to get:

384m=r

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Example Question #2 : How To Find The Length Of A Radius

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be $169 \pi m^2$ .

What is the radius of the crater?

Possible Answers:

Cannot be determined from the information provided

26m

15.5m

13m

Correct answer:

13m

Explanation:

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be $169 \pi m^2$ .

What is the radius of the crater?

To solve this, we need to recall the formula for the area of a circle.

$A=\pi r^2$

Now, we know A, so we just need to plug in and solve for r!

$169 \pi m^2=\pi r ^2$

Begin by dividing out the pi

169m^2=r^2

Then, square root both sides.

$r=\sqrt{169m^2}=13m$

So our answer is 13m.

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ISEE Upper Level Math : How to find the length of a radius

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Length Of A Radius

Example Question #1 : Radius

Example Question #2 : Radius

Example Question #2 : How To Find The Length Of A Radius

Example Question #3 : How To Find The Length Of A Radius

Example Question #2 : How To Find The Length Of A Radius

All ISEE Upper Level Math Resources

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