Circumference - GED Math

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Question

Give the circumference of a circle with radius 6. Round to the nearest tenth.

Answer

The circumference of a circle can be found using this formula:

$C = 2 \pi r$

Where $\pi \approx 3.14$

Substitute and use $\pi = 3.14$ , since we are rounding:

$C = 2 \cdot 3.14 \cdot 6 = 37.68$

Round this to .

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Question

A car whose tires have diameter 30 inches moves at a rate of 24 miles per hour. How many revolutions will each tire make in one minute (nearest whole number)?

Answer

We will convert all linear distances to feet and all times to minutes.

The tires have diameter 30 inches, which is equal to $30 \div 12 = 2.5$ feet. Their circumference will be $\pi$ times this, or $2.5 \pi$ feet.

The car moves at a rate of 25 miles per hour, which is equivalent to

$24 \times \frac{5,280}{ 60} = 2,112$ feet per minute.

The number of revolutions each tire makes is the distance traveled divided by the circumference of the tire, which is

$\frac{ 2,112 }{2.5 \pi} \approx \frac{ 2,112 }{7.8540} \approx 269$ .

Each tire revolves about 269 times in the course of one minute.

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Question

What is the circumference of a circle with a diameter of 10 inches?

Answer

The equation for the circumference of a circle is $C=2r\pi$ , where is the radius of the circle. The radius is half the diameter, or 5 inches.

$C=2(5)\pi$

$C=10\pi$

$\pi=3.14$

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Question

What is the circumference of a circle with radius 3?

Answer

The equation for circumference of a circle is $C=2\pi r$ .

Plug in the given radius value and solve:

$C=2(3)\pi$

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Question

What is the circumference of a circle given the radius is 7?

Answer

The equation of circumference of a circle can be found using $C=2\pi r$ . By substituting in our radius of 7 we can solve for C.

$C=2(7)\pi$

$C=14\pi$

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Question

What is the circumference of a circle with a diameter of 40?

Answer

To find the circumference given the diameter we use the equation:

$C=D\pi$

Then we substitute 40 in for our diameter:

$C=40\pi$

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Question

Find the radius of a circle given that the circumference is $24\pi$ .

Answer

The equation of the circumference of a circle is as follows:

$C=2\pi r$

Now we substitute in our circumference and solve for radius:

$24\pi=2\pi r$

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Question

What is the circumference of a circle with a radius of 4?

Answer

We use the equation for the circumference of a circle: $C=2\pi r$

Now we substitute in our radius of 4:

$C=2(4)\pi$

$C=8\pi$

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Question

If the area of a circle is $81\pi$ , what is its circumference?

Answer

To solve this, you should first figure out your radius. Remember that the area of a circle is defined as:

$A=\pi r^2$

For your data, you know that this is:

$81\pi=\pi r^2$

Solving for , you get:

, or

Now, recall that the circumference of a circle is defined as:

$C=2\pi r$

For your data, this is:

$C=2\pi * 9 = 18\pi$

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Question

The area of a sector of a circle with a degree angle is $4\pi$ . What is the circumference of this circle?

Answer

A degree angle represents one fourth of a full circle. Therefore, the total area of this circle is $4 * 4\pi$ or $16\pi$ . Now, recall your area formula:

$A=\pi r^2$

For your data, this means:

$16\pi = \pi r^2$

Solving for , you get:

or

Now, the circumference of a circle is defined as:

$C=2\pi r$

For your data, this is:

$C=24\pi=8\pi$

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Question

What is the circumference of the circle with an area of 5?

Answer

Write the formula for the area of a circle.

$A =\pi r^2$

Substitute the area.

$5 =\pi r^2$

Divide by pi on both sides.

$\frac{5}{\pi } =\frac{\pi r^2}{\pi }$

$r^2 = \frac{5}{\pi}$

Square root both sides.

$\sqrt{r^2} = \sqrt{\frac{5}{\pi}}$

$r = \sqrt{\frac{5}{\pi}}$

Write the circumference formula for the circle, and substitute the radius.

$C=2\pi r =2\pi \sqrt{\frac{5}{\pi}} = 2\pi \frac{\sqrt{5}}{\sqrt{\pi}}$

Since $\pi = (\sqrt{\pi} \cdot \sqrt{\pi})$ , we can eliminate the denominator by rewriting $\pi$ .

$2\pi \frac{\sqrt{5}}{\sqrt{\pi}} = 2(\sqrt{\pi}\cdot \sqrt{\pi}) \frac{\sqrt{5}}{\sqrt{\pi}} = 2\sqrt{\pi}\cdot \sqrt{5}$

The answer is: $2\sqrt{5\pi}$

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Question

Find the circumference of a circle with an area of $12\pi$ .

Answer

Write the formula for the area of a circle, and substitute the area into the formula.

$A=\pi r^2$

$12\pi =\pi r^2$

Divide by pi on both sides.

$\frac{12\pi }{\pi}=\frac{\pi r^2}{\pi}$

Square root both sides.

$\sqrt{r^2 }= \sqrt{12}$

$r=2\sqrt{3}$

Write the formula for the circumference of the circle.

$C=2\pi r$

Substitute the radius into the equation.

$C=2\pi (2\sqrt3) = 4\pi \sqrt3$

The answer is: $4\pi \sqrt3$

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Question

Find the circumference of a circle with a diameter of $5\pi^2$ .

Answer

Write the formula for the circumference.

$C=\pi D$

Substitute the diameter into the equation.

$C=\pi (5\pi^2) = 5\pi ^3$

The answer is: $5\pi ^3$

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Question

Find the circumference of a circle with a diameter of 14cm.

Answer

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 14cm. So, we will substitute. We get

$C = \pi \cdot 14\text{cm}$

$C = 14\pi \text{ cm}$

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Question

Identify the circumference of the circle with an area of $12 \pi$ .

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area.

$12\pi=\pi r^2$

Square root both sides to find the radius.

$\sqrt{r^2}=\sqrt{12}$

$r=\sqrt{12} = \sqrt{4}\times \sqrt{3} = 2\sqrt{3}$

Write the formula for the circumference of the circle.

$C=2\pi r = 2\pi(2\sqrt{3}) = 4\pi \sqrt{3}$

The answer is: $4\pi \sqrt{3}$

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Question

What is the circumference of a circle with a diameter of $2\sqrt2$ ?

Answer

Write the formula for the circumference of a circle.

$C=\pi D$

Substitute the diameter into the equation.

$C=\pi 2\sqrt2$

The answer is: $2\pi \sqrt{2}$

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Question

Determine the circumference of a circle with a radius of $\frac{\pi}{4}$ .

Answer

Write the formula for the circumference of a circle.

$C=\2\pi r$

Substitute the radius.

$C=\2\pi (\frac{\pi}{4}) = \frac{\pi ^2}{2}$

The answer is: $\frac{\pi ^2}{2}$

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Question

Find the circumference of a circle with a diameter of 9cm.

Answer

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 9cm. So, we will substitute. We get

$C = \pi \cdot 9\text{cm}$

$C = 9\pi \text{ cm}$

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Question

What is the circumference of a circle with an area of $12\pi$ ?

Answer

For this question, you need to first use the area to calculate your circle's radius. From that, you can then calculate the circumference of the circle. Recall that the area of a circle is defined as:

$A=\pi r^2$

For your data, this means:

$12\pi=\pi r^2$

Solving for , you get...

$r=\sqrt{12}=\sqrt{43}=2\sqrt{3}$

Now, the circumference of a circle is calculated as:

$C=2\pi r$

For your data, this is:

$C=2\pi2\sqrt{3}=4\pi\sqrt{3}$

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Question

Evaluate the circumference of a circle if the radius is $\frac{3}{4}$ .

Answer

Write the equation for the circumference of a circle.

$C=2\pi r$

Substitute the radius and solve.

$C=2\pi (\frac{3}{4}) = \frac{6}{4}\pi = \frac{3}{2}\pi$

The answer is: $\frac{3}{2}\pi$

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