Circumference of a circle

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7th Grade Math › Circumference of a circle

Questions 1 - 10

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

$8\pi ; in$

$12\pi ; in$

$4\pi ; in$

$6\pi ; in$

$10\pi ; in$

Explanation

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:

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

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

$9\pi$

$81\pi$

$18\pi$

$27\pi$

$90\pi$

Explanation

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.

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

(Round your answer to the nearest tenth.)

$32.7\textup{ in}$

$10.4\textup{ in}$

$49.3\textup{ in}$

$22.8\textup{ in}$

$16.3\textup{ in}$

Explanation

The circumference is given by the formula:

$C=2\pi r$

where is the radius.

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

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

Circle_12d

$12\pi\ \text{inches}$

$6\pi\ \text{inches}$

$38\ \text{inches}$

$44\ \text{inches}$

none of these

Explanation

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 $C=12\pi \hspace\ \text{inches}$

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

$16\pi$

$8\pi$

$28\pi$

$16\pi^{2}$

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:

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

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

$14\pi$

$49\pi$

$7\pi$

$196\pi$

Explanation

The circumference can be solved using the following equation:

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

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

$14\pi$

$49\pi$

Explanation

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

$C=2\pi{r}=2*\pi*7=14\pi$

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.

Find the circumference of a circle with a radius of .