GMAT Math : Circles

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Example Question #1 : Calculating Circumference

If the radius of a circle is $5\:cm$ , what is its circumference?

Possible Answers:

$10\pi\:cm$

$2.5\pi\:cm$

$5\pi\:cm$

$25\pi\:cm$

$15\pi\:cm$

Correct answer:

$10\pi\:cm$

Explanation:

Using the formula for the circumference of a circle, we can plug in the given value for the radius and calculate our solution:

$C=2\pi r=2\pi (5\:cm)=10\pi\:cm$

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Example Question #8 : Calculating Circumference

Megan, a civil engineer, is designing a roundabout for the city of Madison. She knows that the distance from the edge of the roundabout to the center must be 25 meters. Help Megan find the circumference of the roundabout.

Possible Answers:

$50\pi m$

$12.5\pi m$

$5\pi m$

$225\pi m$

Correct answer:

$50\pi m$

Explanation:

We are asked to find circumference. In order to do so, look at the following formula:

$C=2\pi r$

Where r is our radius and C is our circumference.

We are indirectly told that our radius is 25 meters, plug it in to get our answer:

$C=2\pi 25m=50 \pi m$

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Example Question #9 : Calculating Circumference

A circle has radius $\pi ^{t}$ . Give its circumference.

Possible Answers:

$\pi ^{2t+1}$

$\pi ^{t+2}$

$2 \pi ^{t+1}$

$\pi ^{t+1}$

$2 \pi ^{2t}$

Correct answer:

$2 \pi ^{t+1}$

Explanation:

The circumference of a circle is found using the following formula:

$C =2 \pi r$

Set $r= \pi ^{t}$ :

$C =2 \pi \cdot \pi ^{t} = 2 \cdot \pi ^{1} \pi ^{t} = 2 \pi ^{t+1}$

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Example Question #1 : Calculating The Length Of The Diameter

A square is inscribed inside a circle. The square has an area of 100. Find the area of the circle.

Possible Answers:

$75\pi$

$12.5\pi$

$50\pi$

$25\pi$

Correct answer:

$50\pi$

Explanation:

Since the square is inscribed inside the circle, then the length of the diagonal of the square will be the diameter of the circle. The area of a circle is given as $A=\pi r^2$ and

$\frac{diameter}{2}=radius \Rightarrow r=\frac{d}{2}.$

Substituting the diameter into the equation of the area we get

$A=\pi*r^2=\pi*\left (\frac{d}{2}\right )^2=\frac{\pi*d^2}{4}.$

So if we find the diagonal of the square, then we can find the area of the circle. To find the diagonal of the square we use the fact that the area of a square is A=s^2 where is the side of the square. Since the area is 100, then the length of the square is 10. The diagonal is then given by

$diagonal=\sqrt{10^2+10^2}=\sqrt{200}=10\sqrt{2}.$

Substituting this into our equation for the area of a circle, we get

$A=\frac{\pi*(10\sqrt{2})^2}{4}=\frac{\pi*100*2}{4}=\pi*25*2=50\pi$

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Example Question #1 : Calculating The Length Of The Diameter

Find the center of the circle that has a diameter with endpoints at (-4,4) and (0,2) .

Possible Answers:

$\dpi{100} \small (2,-3)$

$\dpi{100} \small (-2,3)$

$\dpi{100} \small (-2,6)$

$\dpi{100} \small (-4,3)$

$\dpi{100} \small (0,0)$

Correct answer:

$\dpi{100} \small (-2,3)$

Explanation:

$midpoint = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} ) = (\frac{-4 + 0}{2}, \frac{4 + 2}{2}) = (\frac{-4}{2}, \frac{6}{2}) = (-2, 3)$

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Example Question #3 : Calculating The Length Of The Diameter

Consider the Circle :

Circle3

(Figure not drawn to scale.)

If is the center of the circle and is a point on its circumference, what is the length of the diameter of the circle?

Possible Answers:

$45\:m$

$225\:m$

$15\:m$

$30\:m$

$60\:m$

Correct answer:

$30\:m$

Explanation:

This problem provides you with a circle and gives you clues that line is the radius. A line that passes through the center and ends on the circumference of the circle is the radius of the circle. In this case, our radius is 15 meters. Diameter is simply twice the radius, so our diameter is 30 meters.

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Example Question #4 : Calculating The Length Of The Diameter

A circle has a circumference of $16\pi\:cm$ . What is the diameter of the circle?

Possible Answers:

$16\:cm$

$8\:cm$

$32\:cm$

$24\:cm$

$4\:cm$

Correct answer:

$16\:cm$

Explanation:

We can find the diameter of the circle using the formula for circumference:

$C=2\pi r$

First, we must recognize that the radius is just half of the diameter, which allows us to express the formula in terms of diameter:

$C=2\pi r=2\pi (\frac{d}{2})=\pi d$

Now we can just plug in the given circumference and solve for the diameter:

$C=\pi d\rightarrow 16\pi\:cm=\pi d\rightarrow d=16\:cm$

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Example Question #5 : Calculating The Length Of The Diameter

If the area of a circle is $9\pi\:cm^2$ , what is the diameter of the circle?

Possible Answers:

$3\:cm$

$4\:cm$

$6\:cm$

$9\:cm$

$5\:cm$

Correct answer:

$6\:cm$

Explanation:

We are given the area of the circle, so we will need to use the formula for area to calculate its diameter:

$A=\pi r^2$

First, we must express the formula in terms of diameter instead of radius. The radius is just half of the diameter, so we can write:

$A=\pi r^2=\pi (\frac{d}{2})^2=\frac{\pi }{4}d^2$

Now we can simply plug in the given area and solve for the diameter:

$A=\frac{\pi }{4}d^2\rightarrow 9\pi\:cm^2=\frac{\pi }{4}d^2\rightarrow d^2=36\:cm^2\rightarrow d=6\:cm$

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Example Question #6 : Calculating The Length Of The Diameter

A given circle has an area of $81\pi$ . What is the length of its diameter?

Possible Answers:

4.5

Not enough information provided

Correct answer:

Explanation:

The area of a circle is defined by the equation $A=\pi r^{2}$ , where is the length of the circle's radius. The radius, in turn, is defined by the equation $r=\frac{d}{2}$ , where is the length of the circle's diameter.

Given $A=81\pi$ , we can deduce that $r^{2}=81$ and therefore r=9 . Then, since $r=\frac{d}{2}$ , d=2r=2(9)=18 .

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Example Question #7 : Calculating The Length Of The Diameter

A given circle has a radius of 17cm . What is the diameter of the circle?

Possible Answers:

$34cm^{2}$

34cm

44cm

$\frac{17}{2}cm$

20cm

Correct answer:

34cm

Explanation:

By definition, the length of a circle's diameter is twice the length of the circle's radius , or d=2r . Since r=17cm , d=2(17cm)=34cm .

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GMAT Math : Circles

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating Circumference

Example Question #8 : Calculating Circumference

Example Question #9 : Calculating Circumference

Example Question #1 : Calculating The Length Of The Diameter

Example Question #1 : Calculating The Length Of The Diameter

Example Question #3 : Calculating The Length Of The Diameter

Example Question #4 : Calculating The Length Of The Diameter

Example Question #5 : Calculating The Length Of The Diameter

Example Question #6 : Calculating The Length Of The Diameter

Example Question #7 : Calculating The Length Of The Diameter

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