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ISEE Upper Level Math : How to find circumference

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Example Question #51 : Circles

What is the circumference of a circle with a radius equal to ?

Possible Answers:

$14\pi$

$7\pi$

$196\pi$

$49\pi$

Correct answer:

$14\pi$

Explanation:

The circumference can be solved using the following equation:

$C=2r\pi=2(7)\pi=14\pi$

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Example Question #1 : Circumference Of A Circle

The radius of a circle is t^2 . Give the circumference of the circle in terms of .

Possible Answers:

$2\pi t^2$

$2\pi t$

$\pi t$

$4\pi t^2$

$\pi t^2$

Correct answer:

$2\pi t^2$

Explanation:

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

$Circumference =2\pi r=2\pi t^2$

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Example Question #191 : Plane Geometry

The area of a circle is 25t^2 . Give the circumference of the circle in terms of .

Let $\pi=3.14$ .

Possible Answers:

15t

20t^2

17.71 t^2

17.71t

20t

Correct answer:

17.71t

Explanation:

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

$Area=\pi r^2\Rightarrow 25t^2=\pi r^2\Rightarrow r^2=\frac{25t^2}{\pi}$

$\Rightarrow r=\frac{5t}{\sqrt{\pi}}=\frac{5t}{\sqrt{3.14}}\approx 2.82t$

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

$Circumference =2\pi r\Rightarrow Circumference =2\times 3.14\times 2.82t=17.71t$

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Example Question #1 : Circumference Of A Circle

What is the circumference of a circle with a radius of ?

Possible Answers:

$8\pi$

$16\pi^{2}$

$28\pi$

$16\pi$

Correct answer:

$16\pi$

Explanation:

The circumference can be solved using the following equation:

$C=2r\pi$

Where represents the radius. Therefore, when we substitute our radius in we get:

$=2(8)\pi =16\pi$

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Example Question #1 : Circumference Of A Circle

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius inches; the width of the rectangle is $8 \pi$ inches. What is the length of the rectangle?

Possible Answers:

$22 \pi$ inches

$44 \pi$ inches

$7\pi$ inches

$14 \pi$ inches

$(30 - 8 \pi )$ inches

Correct answer:

$22 \pi$ inches

Explanation:

The circumference of a circle with radius inches is

$C = 2 \pi r = 2 \pi \cdot 30 = 60 \pi$ inches.

The perimeter of the rectangle is therefore $60 \pi$ inches. To find its length, substitute $W = 8\pi$ and $P = 60\pi$ into the equation and solve for :

2 L + 2W = P

$2 L + 2 \cdot 8 \pi = 60 \pi$

$2 L + 16 \pi = 60 \pi$

$2 L + 16 \pi - 16 \pi = 60 \pi - 16 \pi$

$2 L =44 \pi$

$2 L \div 2=44 \pi \div 2$

$L = 22\pi$ inches

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Example Question #2 : How To Find Circumference

Sector

The area of the shaded region in the above diagram is $72 \pi$ . Give the circumference of the circle.

Possible Answers:

$18 \pi$

$72 \pi$

$36 \pi$

$8 \pi$

Correct answer:

$36 \pi$

Explanation:

The shaded region is an $80 ^{\circ }$ sector; this represents

$\frac{80}{360} = \frac{80 \div 40 }{360\div 40} = \frac{2}{9}$

of the circle. The area of the region is therefore

$A = \frac{2}{9} \cdot \pi r^{2}$ ,

where is the radius. Setting $A = 72 \pi$ and solving for :

$\frac{2}{9} \cdot \pi r^{2} = 72 \pi$

$\frac{9}{2 \pi} \cdot \frac{2}{9} \cdot \pi r^{2} =\frac{9}{2 \pi} \cdot 72 \pi$

$r^{2} =324$

$r = \sqrt{324 } =18$

The circumference of a circle is its radius multiplied by $2 \pi$ , or

$C = 2 \pi r = 2 \pi \cdot 18 = 36 \pi$

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Example Question #1 : How To Find Circumference

A circle has a radius of 5 miles, what is its circumference?

Possible Answers:

$10\pi mi$

314 mi

$25 \pi mi$

125 mi

Correct answer:

$10\pi mi$

Explanation:

A circle has a radius of 5 miles, what is its circumference?

To find circumference, use the following formula:

$Circumference=2\pi r$

Where r is our radius.

Plug in 5 miles to get our answer:

$Circumference=2\pi (5mi)=10 \pi mi$

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Example Question #2 : How To Find Circumference

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the circumference of the stamping surface?

Possible Answers:

Cannot be determined from the information provided.

9.25cm

$7 \pi cm$

12.25 cm

Correct answer:

$7 \pi cm$

Explanation:

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the circumference of the stamping surface?

Find circumference via the following:

$C=2 \pi r$

Where r is our radius, which is 3.5 cm.

$C=2(3.5cm) \pi =7\pi cm$

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Example Question #1 : How To Find Circumference

You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?

Possible Answers:

$18 \pi in$

$18 \pi in^2$

$36 \pi in$

$81 \pi in^2$

Correct answer:

$18 \pi in$

Explanation:

You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?

Begin with the formula for circumference of a circle.

$C=2 \pi r$

Next, plug in our "r" and solve for C

$C= 2 \pi (9in)=18 \pi in$

So, we have our answer!

$18 \pi in$

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Example Question #6 : How To Find Circumference

Find the circumference of a circle with a radius of 4cm.

Possible Answers:

$8 \pi \text{ cm}$

$4\pi \text{ cm}$

$2\pi \text{ cm}$

$16\pi \text{ cm}$

$12\pi \text{cm}$

Correct answer:

$8 \pi \text{ cm}$

Explanation:

To find the circumference of a circle, we will use the following formula:

$C = 2 \cdot \pi \cdot r$

where r is the radius of the circle.

Now, we know the radius of the circle is 4cm.

Knowing this, we can substitute into the formula. We get

$C = 2 \cdot \pi \cdot 4\text{cm}$

$C = 2\pi \cdot 4\text{cm}$

$C = 8\pi \text{ cm}$

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ISEE Upper Level Math : How to find circumference

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #51 : Circles

Example Question #1 : Circumference Of A Circle

Example Question #191 : Plane Geometry

Example Question #1 : Circumference Of A Circle

Example Question #1 : Circumference Of A Circle

Example Question #2 : How To Find Circumference

Example Question #1 : How To Find Circumference

Example Question #2 : How To Find Circumference

Example Question #1 : How To Find Circumference

Example Question #6 : How To Find Circumference

All ISEE Upper Level Math Resources

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