The circumference of a circle is the length of the path that goes around the circle.
The circumference is usually denoted by the letter
One important fact about the circumference is that, for any circle, no matter how small or large it is, the ratio of circumference to diameter is a fixed number! Specifically,
This important irrational number is called pi (pronounced "pie") and we use the Greek letter to express it. So, we can calculate the circumference by using the following formula:
Here, our circle has diameter so its circumference is rounded to three decimal digits.
Since the diameter is twice as long as the radius (), we can also write the formula for the circumference as
What is the circumference of a circle with a diameter of
We use the formula and get
This is the exact answer. If we want an approximate answer, say rounded to three decimal places, we can use the approximation and we get
What is the circumference of a circle with a diameter of $\dfrac{16}{\pi}\,\textrm{cm}?$
|
a
|
$16 \,\textrm{cm}$ |
|
b
|
$32 \,\textrm{cm}$ |
|
c
|
$16 \pi \,\textrm{cm}$ |
|
d
|
$32 \pi \,\textrm{cm}$ |
|
e
|
$6 \pi \,\textrm{cm}$ |
What is the circumference of a circle with a diameter of $8\,\textrm{cm}?$
|
a
|
$ 8 \pi \,\textrm{cm}$ |
|
b
|
$ 16 \pi \,\textrm{cm}$ |
|
c
|
$\dfrac{3}{2} \pi \,\textrm{cm}$ |
|
d
|
$ 3 \pi \,\textrm{cm}$ |
|
e
|
$\dfrac{7}{2} \pi \,\textrm{cm}$ |
What is the circumference of a circle with a radius of
We use the formula to get
What is the circumference of a circle with a radius of $\dfrac{\sqrt{2}}{2} \,\textrm{cm}?$
|
a
|
$\dfrac{\sqrt{2}}{2} \,\textrm{cm}$ |
|
b
|
$\sqrt{2} \,\textrm{cm}$ |
|
c
|
$2 \pi \,\textrm{cm}$ |
|
d
|
$\dfrac{\sqrt{2}}{2} \pi \,\textrm{cm}$ |
|
e
|
$\sqrt{2} \pi \,\textrm{cm}$ |
What is the circumference of a circle with a radius of $8 \,\textrm{cm}?$
|
a
|
$16\,\textrm{cm}$ |
|
b
|
$4\,\textrm{cm}$ |
|
c
|
$16 \pi\,\textrm{cm}$ |
|
d
|
$6 \pi\,\textrm{cm}$ |
|
e
|
$32 \pi\,\textrm{cm}$ |
What is the radius of a circle with a circumference of
We use the formula for the circumference and solve for So, we have
What is the diameter of a circle with a circumference of $6 \pi?$
|
a
|
$3\pi$ |
|
b
|
$6 \pi$ |
|
c
|
$6$ |
|
d
|
$3$ |
|
e
|
$12$ |
What is the radius $r$ of a circle with a circumference of $16\,\textrm{km}?$
|
a
|
$\dfrac{\sqrt{5}}{4} \pi\,\textrm{km}$ |
|
b
|
$8\,\textrm{km}$ |
|
c
|
$\dfrac{\sqrt{2}}{\pi}\,\textrm{km}$ |
|
d
|
$\dfrac{8}{\pi}\,\textrm{km}$ |
|
e
|
$\sqrt{3}\,\textrm{km}$ |
Carol has to wrap a rope around a circular column whose diameter is What length of the rope will wrap the column perfectly?
The length of the rope needed to wrap around the column is its circumference.
The formula for the circumference of a circle is , where is the diameter.
Therefore, we have
What length of fence is needed to border a circular plot of land with a diameter of $30\,\textrm{m}?$
|
a
|
$60\pi\,\textrm{m}$ |
|
b
|
$30\,\textrm{m}$ |
|
c
|
$30\pi\,\textrm{m}$ |
|
d
|
$\pi\,\textrm{m}$ |
|
e
|
$15\pi\,\textrm{m}$ |
Ken's tree has a diameter of $4\,\textrm{ft}.$ What length of chain does Ken need for it to wrap around the tree perfectly?
|
a
|
$\pi\,\textrm{ft}$ |
|
b
|
$8\,\textrm{ft}$ |
|
c
|
$4\pi\,\textrm{ft}$ |
|
d
|
$8\pi\,\textrm{ft}$ |
|
e
|
$2\pi\,\textrm{ft}$ |