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ISEE Upper Level Math : Radius

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Example Questions

Example Question #41 : Radius

Let $\pi = 3.14$

Find the circumference of a circle with a radius of 8in.

Possible Answers:

$43.96\text{in}$

$56.52\text{in}$

$25.12\text{in}$

$50.24\text{in}$

$200.96\text{in}$

Correct answer:

$50.24\text{in}$

Explanation:

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

$C = 2\pi r$

where r is the radius of the circle.

Now, we know the radius of the circle is 8in.

We also know that $\pi = 3.14$ .

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

$C = 2 \cdot 3.14 \cdot 8\text{in}$

$C = 16\text{in} \cdot 3.14$

$C = 50.24\text{in}$

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Example Question #42 : Radius

You want to ice skate around the outer edge of a circular pond (the water is frozen, because it is January and you live in Wisconsin). If the pond has a radius of 35 meters, how far will you skate in one lap around the pond?

Possible Answers:

$70 \pi m$

Not enough information to complete.

$1,225 \pi m$

450 m

Correct answer:

$70 \pi m$

Explanation:

Let's begin by realizing what we are being asked for. They want us to find the total distance we will travel in one lap around the pond. This sounds like circumference, because we are going one full distance around the outside of the circle.

The formula for circumference is as follows.

$C=2 \pi r$

Now, we have r, so just plug in and solve.

$C=2 \pi (35m)=2*35 m \pi=70 \pi m$

So, our answer is:

$70 \pi m$

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Example Question #43 : Radius

You are conducting fieldwork, when you find a tree whose radius at chest height is . What is the circumference of the tree at chest height?

Possible Answers:

$5.05 \pi m$

$4.25 \pi m$

$2.25 \pi m$

$3.0 \pi m$

Correct answer:

$3.0 \pi m$

Explanation:

You are conducting fieldwork, when you find a tree whose radius at chest height is . What is the circumference of the tree at chest height?

The formula for circumference of a circle is:

$C= 2 \pi r$

We have r, so simply plug it in and solve:

$C=2 \pi (1.5m)=3 \pi m$

So, our answer is $3 \pi m$

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Example Question #44 : Radius

Find the circumference of a circle with a diameter of 18cm.

Possible Answers:

$9\pi \text{ cm}$

$18\pi \text{ cm}$

$36\pi \text{ cm}$

$52\pi \text{ cm}$

$24\pi \text{ cm}$

Correct answer:

$18\pi \text{ cm}$

Explanation:

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

$C = \pi d$

where d is the diameter of the circle.

Now, we know the diameter of the circle is 18cm. So, we will substitute. We get

$C = \pi \cdot 18\text{cm}$

$C = 18\pi \text{ cm}$

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Example Question #45 : Radius

Find the circumference of a circle with a radius of 10in.

Possible Answers:

$100\pi \text{ in}$

$75\pi \text{ in}$

$20\pi \text{ in}$

$50\pi \text{ in}$

$25\pi \text{ in}$

Correct answer:

$20\pi \text{ in}$

Explanation:

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

$C = 2\pi r$

where r is the radius of the circle.

Now, we know the radius of the circle is 10in.

So, we get

$C = 2 \cdot \pi \cdot 10\text{in}$

$C = 20\text{in} \cdot \pi$

$C = 20\pi \text{ in}$

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Example Question #46 : 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 circumference of the crater?

Possible Answers:

$26 \pi m$

26 m^2

39 m

26m

Correct answer:

$26 \pi m$

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 circumference 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.

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

Next, plug our answer into the circumference formula.

$C=2 \pi r = 2 (13m) \pi =26 \pi m$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Radius

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #41 : Radius

Example Question #42 : Radius

Example Question #43 : Radius

Example Question #44 : Radius

Example Question #45 : Radius

Example Question #46 : Radius

All ISEE Upper Level Math Resources

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