Circumference of a Circle - Pre-Algebra

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

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The circumference can be solved using the following equation:

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

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?

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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 :

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

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

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

$2 L =44 \pi$

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

$L = 22\pi$ inches

What is the circumference of a circle with an area equal to $81\pi$ ?

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Using the area, solve for the radius:

Divide by $\pi$ :

Take the square root:

$$\sqrt{81}$=9=r$

Plug this radius into the formula for the circumference:

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

Becky's house is surrounded by a circular lake that Becky runs around each day. If Becky wants to figure out the distance she runs around the lake, what formula should Becky use?

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Becky should use the circumfrence formula to find the distance she runs of a lake.

Correct Answer: $C=2\Pi r$

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

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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:

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

Determine the circumference of the circle if the radius is 20.

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Write the formula for circumference.

$C=2\pi r$

Substitute the radius and solve.

$C=2\pi(20) = 40\pi$

Given the area of the circle is $9\pi$ , what is the circumference of the circle?

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Write the formula for the area of a circle.

$A=\pi $r^2$$

Substitute the area.

$9\pi=\pi $r^2$$

Write the circumference of the circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi (3) = 6\pi$

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

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Write the formula for the circumference of a circle.

$C=\pi D = 2\pi r$

Substitute the diameter.

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

Find the circumference of a circle with an area of .

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Write the area formula in order to find the radius.

$A=\pi $r^2$$

Substitute the area.

$\pi ^2=\pi $r^2$$

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

Write the circumference formula.

$C=2\pi r$

Substitute the radius.

$C=2\pi $\sqrt{\pi}$$

Determine the circumference of the circle if the radius is $2\pi$ .

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Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the radius into the formula.

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

Find the circumference of a circle with a radius of $\sqrt2$ .

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Write the formula to find the circumference of a circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi $\sqrt{2}$$

Find the circumference of a circle with an area of 5.

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Write the formula for the area of a circle.

$A=\pi $r^2$$

Substitute the area to find the radius.

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

$5=\pi $r^2$$

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

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

Write the formula to find the circumference of the circle.

$C=2\pi r$

Substitute the radius.

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

If $\pi = 3.14$ find the circumference of a circle with a diameter of 10 inches.

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To solve, we will use the formula for circumference of a circle. The formula is

$C = 2 \pi r$

where $r = $\text{ radius}$$ . We know that the diameter of the circle is 10 inches. To find the radius, we simply divide by 2.

Therefore,

We know $\pi = 3.14$ , so we will substitute. We get

$C = 2 \cdot 3.14 \cdot 5 $\text{ inches}$$

$C = 31.4 $\text{ inches}$$

Therefore, the circumference of the circle is 31.4 inches.

Find the circumference of a circle with a radius of 6cm.

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The formula to find the circumference of a circle is

$C = \pi d$

where d is the diameter. We know the radius is 6cm. We also know to find the diameter, we take two times the radius. Therefore, the diameter is 12cm. So, substituting into the formula, we get

$C = \pi \cdot 12$

or

$C = 12\pi$

Therefore, the circumference of the cirlce is $12\pi$ .

A circle has a radius of . What is its circumference?

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The formula for the circumference of a circle is

$C=2\pi r$ .

So, we simply plug in the radius of in order to solve for the circle's circumference:

$C=2\pi (19)$

$C=38\pi$

Therefore, the circumference of ths circle is $38\pi$ .

What is the distance around a silo, if the distance from the center of the silo to the outside is ?

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What is the distance around a silo, if the distance from the center of the silo to the outside is ?

Picture a silo, its base is a circle.

This problem want the circumference of that circle. It gives us the distance from the center to the outside of the circle, aka the radius.

Find circumference via the following formula:

$Circumference=2 \pi r$

$C=2*8 \pi =16\pi m$

So the distance is:

$16\pi m$

Alfredo ran laps around his track. He had just learned in math about circumference and was wondering what the circumference of his circular track was. He knows that the diameter of his track is 100 feet. What is the circumference of Alfredo's track?

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The only thing that needs to be known for this question is the equation for circumference which is:

$\pi$

Therefore your answer to this problem is simply

$100\pi$

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

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The circumference can be solved using the following equation:

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

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?

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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 :

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

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

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

$2 L =44 \pi$

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

$L = 22\pi$ inches

What is the circumference of a circle with an area equal to $81\pi$ ?

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Using the area, solve for the radius:

Divide by $\pi$ :

Take the square root:

$$\sqrt{81}$=9=r$

Plug this radius into the formula for the circumference:

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