Pre-Algebra - Circumference of a Circle

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

$18\pi$

$9\pi$

$36\pi$

$4.5\pi$

Explanation

Using the area, solve for the radius:

$A=r^2\pi$

$81\pi=r^2\pi$

Divide by $\pi$ :

Take the square root:

$\sqrt{81}=9=r$

Plug this radius into the formula for the circumference:

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

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:

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

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?

$C=2\Pi r$

$C=\Pi r^{2}$

$P=d\Pi$

$C=l\cdot w$

None of the other answers

Explanation

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

Correct Answer: $C=2\Pi r$

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

$2\pi ^2$

$4\pi$

$4\pi ^2$

$8\pi$

$8\pi ^2$

Explanation

Write the formula for the circumference of a circle.

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

Substitute the diameter.

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

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

$4\pi ^2$

$4\pi$

$2\pi ^2$

$4\pi ^3$

$8\pi$

Explanation

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 an area of 5.

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

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

$2\sqrt5$

$2\pi\sqrt5$

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

Explanation

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.

$31.4\ inches$

$62.8\ inches$

$78.5\ inches$

$15.7\ inches$

$47.1\ inches$

Explanation

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.

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

$38\pi$

$361\pi$

$19\pi$

$21\pi$

Not enough information given

Explanation

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 $38\pi$ .

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?

$22 \pi$ inches

$44 \pi$ inches

$14 \pi$ inches

$7\pi$ inches

$(30 - 8 \pi )$ inches

Explanation

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 :