Circumference of a circle - Common Core: 7th Grade Math

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Question

Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?

Answer

In order to solve this question, first calculate the length of each side of the room.

The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since $C=\pi d$ , the circumference is simply

$C=9\pi$

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Question

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

Answer

The formula for the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

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Question

What is the circumference of a circle with a radius of $5.2\textup{ in}$ ?

(Round your answer to the nearest tenth.)

Answer

The circumference is given by the formula:

$C=2\pi r$

where is the radius.

$2\pi (5.2)=32.7\ in$

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Question

If this circle has a diameter of 12 inches, what is its circumference?

Answer

Know that the formula for circumference is $C=D\pi$ , where C is the circumference and D is the diameter. It is given that the diameter is 12 inches. Therefore, the circumference is $C=12\pi \hspace\ \text{inches}$

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Question

If a circle has an area of $16\pi ; in^{2}$ , what is the circumference?

Answer

For a circle, the formula for area is $A = \pi r^{2}$ and the formula for circumference is $C=\pi d$ , where is the radius and is the diameter.

Plug the known quantities into the area formula and solve for the radius:

$16\pi =\pi r^{2}$

Now plug this value into the circumference formula to solve:

$C = \pi d = \pi 2r = \pi 2(4) = 8\pi; in$

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Question

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

Answer

The circumference can be solved using the following equation:

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

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Question

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

Answer

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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Question

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

Answer

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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Question

Find the circumference of a circle that has a radius of $\frac{1}{2}$ .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times \frac{1}{2} \times\pi$

Solve.

$\text{Circumference}=\frac{2}{2} \times\pi$

Simplify.

$\text{Circumference}= \pi$

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Question

Find the circumference of a circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 2 \times\pi$

Solve.

$\text{Circumference}=4\times \pi$

Simplify.

$\text{Circumference}=4\pi$

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Question

Find the circumference of the circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 10 \times\pi$

Solve.

$\text{Circumference}=20\times\pi$

Simplify.

$\text{Circumference}=20\pi$

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Question

Find the circumference of a circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 0.9 \times\pi$

Solve.

$\text{Circumference}=1.8\times\pi$

Simplify.

$\text{Circumference}=1.8\pi$

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Question

Find the circumference of a circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 2.4 \times\pi$

Solve.

$\text{Circumference}=4.8\times\pi$

Simplify.

$\text{Circumference}=4.8\pi$

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Question

Find the circumference of a circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 50 \times\pi$

Solve.

$\text{Circumference}=100 \times\pi$

Simplify.

$\text{Circumference}=100\pi$

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Question

Find the circumference of a circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 15 \times\pi$

Solve.

$\text{Circumference}=30 \times\pi$

Simplify.

$\text{Circumference}=30\pi$

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Question

Find the circumference of a circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 14 \times\pi$

Solve.

$\text{Circumference}=28 \times\pi$

Simplify.

$\text{Circumference}=28\pi$

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Question

Find the circumference of a circle with a radius of .

Answer

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 51 \times\pi$

Solve.

$\text{Circumference}=102 \times\pi$

Simplify.

$\text{Circumference}=102\pi$

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Question

Find the circumference of a circle given the radius is 7.

Answer

To solve, simply use the formula for the circumference of a circle. Thus,

$C=2\pi{r}=2\pi7=14\pi$

Another way to similarly solve this problem is to remember that circumference is just pi times the diameter. To find the diameter, remember "di" means two, thus two radii. So, if you multiply the radius by 2, then you have the diameter. Then, just multiply by pi.

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Question

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

Answer

The formula to find the circumference of a cirlce using the radius is:

$C=2\pi r$

The radius is , so we plug that into the formula:

$C=2\pi (3.5)$

$C=7\pi cm$

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Question

What is the circumference of the circle provided?

Answer

In order to solve this problem, we need to recall the formula for the circumference of a circle:

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

The circle in this question provides us with the radius, so we can use the first formula to solve:

$C=2(3)\pi$

Solve:

$C=6\pi\textup{ in}$

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