Circle circumference of a wheel

What defines the circumference of a circle?

The circumference is the distance around a circle. It can be calculated with $\displaystyle C = 2 \pi r$, where $\displaystyle r$ is the radius.

True or false: Circumference is the radius times 2.

False, because the circumference is $\displaystyle C = 2 \pi r$, which includes $\displaystyle \pi$.

How to find the diameter from circumference?

The diameter can be found by dividing the circumference by $\displaystyle \pi$, $\displaystyle d = \\frac{C}{\pi}$.

Fill in the blank: The formula for circumference is _____

$\displaystyle C = 2 \pi r$.

Difference between diameter and radius

The diameter is twice the radius. $\displaystyle d = 2r$.

What is the circumference of a wheel with radius 10 inches?

$\displaystyle C = 2 \pi (10) = 20\pi \approx 62.83$ inches.

True or false: All circles have the same circumference if they have the same radius.

True, because circumference is directly proportional to the radius.

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

$\displaystyle C = \pi d = \pi (12) \approx 37.70$ inches.

Circumference of a circle in terms of diameter

$\displaystyle C = \pi d$.

What is the circumference of a tire with a 15-inch diameter?

$\displaystyle C = \pi (15) \approx 47.12$ inches.

True or false: A larger radius results in a larger circumference.

True, because circumference increases with radius.

Fill in the blank: To calculate circumference, you need the _____ of the circle.

radius or diameter.

What is the relationship between circumference and area?

Area increases with radius, but circumference is linear: $\displaystyle A = \pi r^2$, $\displaystyle C = 2 \pi r$.

How do you convert circumference to radius?

$\displaystyle r = \\frac{C}{2\pi}$.

What happens to circumference if radius is doubled?

Circumference also doubles, because $\displaystyle C = 2\pi(2r) = 4\pi r$.