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ISEE Upper Level Math : Circles

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Example Questions

Example Question #1 : How To Find The Ratio Of Diameter And Circumference

A circle has a radius of . What is the ratio of the diameter to the circumference?

Possible Answers:

2:4

1:3.14

4:25.18

2:8

Correct answer:

1:3.14

Explanation:

The information about the radius is unnecessary to the problem. The equation of the circumference is:

$C=d\pi$

$\pi \approx 3.14$

C=3.14d

Therefore, the circumference is 3.14 times larger than the diameter, and the ratio of the diameter to the circumference is:

1:3.14

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Example Question #2 : Circles

A circle has a radius of . What is the ratio of the diameter to the circumference?

Possible Answers:

1:3.14

4:25.18

4:3.14

2:8

2:4

Correct answer:

1:3.14

Explanation:

The information about the radius is unnecessary to the problem. The equation of the circumference is:

$C=d\pi$

$\pi \approx 3.14$

C=3.14d

Therefore, the circumference is 3.14 times larger than the diameter, and the ratio of the diameter to the circumference is:

1:3.14

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Example Question #1 : Circles

The area of a circle is $25\pi$ . Give the diameter and radius of the circle.

Possible Answers:

diameter = , radius =

diameter = , radius = 2.5

diameter = , radius =

Correct answer:

diameter = , radius =

Explanation:

The area of a circle can be calculated as $Area=\pi r^2$ where is the radius of the circle, and $\pi$ is approximately 3.14 .

$Area=\pi r^2\Rightarrow r^2=\frac{Area}{\pi}$

$\Rightarrow r=\sqrt{\frac{Area}{\pi}}=\sqrt{\frac{25 \pi}{\pi}}=\sqrt{25}\Rightarrow r=5$

To find the diameter, multiply the radius by :

$d=2r=2\times 5=10$

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Example Question #2 : Diameter

If the area of a circle is equal to $36\pi$ , then what is the diameter?

Possible Answers:

$6\pi$

$18\pi$

$12\pi$

$8\pi$

Correct answer:

Explanation:

If the area of a circle is equal to $36\pi$ , then the radius is equal to .

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

Thus, $\pi r^{2}=36 \pi$ .

$r^{2}=36$

r=6

Then the diameter is 12.

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Example Question #1 : Circles

The circumference of a circle is $14\pi$ . Give the diameter of the circle.

Possible Answers:

$14\pi$

$4\pi$

Correct answer:

Explanation:

The circumference can be calculated as $C=2\pi r=\pi d$ , where is the radius of the circle and is the diameter of the circle.

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

$d = \frac{C}{\pi }=\frac{14\pi }{\pi }=14$

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Example Question #1 : Circles

If the value of a radius is $x^{2}-^{\sqrt{x+4}}+2$ , what is the value of the diameter if the value of x=3 ?

Possible Answers:

$11-^{\sqrt{7}$

$11-^{\sqrt{3}$

$22-^{\sqrt{14}$

$22-^{2\sqrt{7}$

Correct answer:

$22-^{2\sqrt{7}$

Explanation:

If the value of a radius is $x^{2}-^{\sqrt{x+4}}+2$ , and the value of x=3 , then the radius will be equal to:

$3^{2}-^{\sqrt{3+4}}+2$

$9-^{\sqrt{7}}+2$

$11-^{\sqrt{7}$

Given that the diameter is twice that of the radius, the diameter will be equal to:

$2(11-^{\sqrt{7}})$

This is equal to:

$22-^{2\sqrt{7}$

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Example Question #135 : Plane Geometry

A series of circles has the following radius values:

6, 9, 5, 4, 3

If the diameter is then calculated for this set, what would be the median diameter?

Possible Answers:

Correct answer:

Explanation:

The median is the middle number in a set when that set is ordered smalles to largest.

When 6, 9, 5, 4, 3 is ordered smallest to largest, we get 3, 4, 5, 6, 9

Here, the median would be .

Given that a diameter is twice the radius, the diamater would be (twice the value of ).

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Example Question #141 : Plane Geometry

The circumference of a circle is $14\pi$ . Give the diameter of the circle.

Possible Answers:

$7\pi$

$8\pi$

Correct answer:

Explanation:

The circumference can be calculated as $Circumference =2\pi r=\pi d$ , where is the radius of the circle and is the diameter of the circle.

$Circumference =\pi d=14 \pi\Rightarrow d=\frac{14\pi}{\pi}=14$

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Example Question #9 : Circles

You have a circular lens with a circumference of $16.67 \pi in$ , find the diameter of the lens.

Possible Answers:

8.33 in

12.45 in

16.67 in

3.14 in

Correct answer:

16.67 in

Explanation:

You have a circular lens with a circumference of $16.67 \pi in$ , find the diameter of the lens.

Begin with the circumference of a circle formula.

$C=2 \pi r$

Now, we know that

2r=d

Because our radius is half of our diameter.

So, we can change our original formula to be:

$C= \pi d$

Now, we can see that all we need to do is divide our circumference by pi to get our diameter.

$\frac{C}{\pi}=d$

Now plug in our known and solve:

$\frac{16.67 \pi in}{\pi}=d=16.67 in$

So our answer is 16.67inches

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Example Question #10 : Circles

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 diameter of the crater?

Possible Answers:

6.5m

52m

26m

19.5m

Correct answer:

26m

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 diameter 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.

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

Now, recall that diameter is just twice the radius.

d=2r=13m (2)=26m

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Circles

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 Ratio Of Diameter And Circumference

Example Question #2 : Circles

Example Question #1 : Circles

Example Question #2 : Diameter

Example Question #1 : Circles

Example Question #1 : Circles

Example Question #135 : Plane Geometry

Example Question #141 : Plane Geometry

Example Question #9 : Circles

Example Question #10 : Circles

All ISEE Upper Level Math Resources

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