GMAT Math : Calculating the length of the diameter

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Example Question #1 : Diameter

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

Possible Answers:

$12.5\pi$

$50\pi$

$75\pi$

$25\pi$

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 : Diameter

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

Possible Answers:

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

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

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

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

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

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 #2 : 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:

$15\:m$

$30\:m$

$225\:m$

$60\:m$

$45\:m$

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 #3 : Diameter

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

Possible Answers:

$32\:cm$

$24\:cm$

$16\:cm$

$8\:cm$

$4\:cm$

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 #3 : Diameter

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

Possible Answers:

$4\:cm$

$3\:cm$

$9\:cm$

$6\:cm$

$5\:cm$

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 #2 : 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 #3 : Calculating The Length Of The Diameter

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

Possible Answers:

44cm

20cm

$34cm^{2}$

34cm

$\frac{17}{2}cm$

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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Example Question #91 : Geometry

The area of a given circle is $10\pi$ . What is the diameter of the circle?

Possible Answers:

$2\sqrt{10}$

$\sqrt{10}$

Not enough information provided

100

Correct answer:

$2\sqrt{10}$

Explanation:

Given $A=10\pi$ , we can deduce that $r^{2}=10$ and therefore $r=\sqrt{10}$ . Then, since $r=\frac{d}{2}$ , $d=2r=2\sqrt{10}$ .

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Example Question #3 : Diameter

While SCUBA diving, Dirk uncovers a strange circular rock formation. He estimates the area of the circular formation to be . Help Dirk find the diameter of the surface.

Possible Answers:

14.02m

6.77m

3.82m

13.54m

Correct answer:

13.54m

Explanation:

While SCUBA diving, Dirk uncovers a strange circular rock formation. He estimates the area of the circular formation to be . Help Dirk find the diameter of the surface.

Recall the formula for area of a circle:

$A=\pi r^2$

Since we know A, we can solve for r

$144=\pi r^2$

Rearranging and simplifing gets our radius to be:

$r\approx6.77m$

We are almost there, but we have one more step to go. We need to double the radius to get the diameter...

$d\approx13.54m$

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Example Question #10 : Calculating The Length Of The Diameter

What is the diameter of a circle with an area of $100\pi units^{2}$

Possible Answers:

20 units

100 units

200 units

10 units

$20\pi units$

Correct answer:

20 units

Explanation:

The area of a circle can be represented by the equation:

$A = \pi r^2$

Therefore:

$\frac{100\pi}{\pi} = \frac{\pi r^2}{\pi} = 100 = r^2$

$\sqrt{r^2} = \sqrt{100} = r = 10$

Since the diameter is twice the radius, d = 20

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GMAT Math : Calculating the length of the diameter

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Diameter

Example Question #1 : Diameter

Example Question #2 : Diameter

Example Question #3 : Diameter

Example Question #3 : Diameter

Example Question #2 : Calculating The Length Of The Diameter

Example Question #3 : Calculating The Length Of The Diameter

Example Question #91 : Geometry

Example Question #3 : Diameter

Example Question #10 : Calculating The Length Of The Diameter

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