# The radius of a circle is 6.5. What is the diameter, circumference, and area?

Dec 31, 2015

Diameter : $13$
Circumference : $13 \pi$
Area : $42 , 25 \pi$

#### Explanation:

The diameter is 2 times the radius so the diameter of this circle is 13.

The circumference of a circle of radius $r$ is given by the formula $2 \pi r$. So here, the circumference of this circle is $13 \pi$.

The area of a circle of radius $r$ is given by the formula $\pi {r}^{2}$. So here, the area of that circle is $6 , {5}^{2} \pi = 42 , 25 \pi$.

Dec 31, 2015

See solution below

#### Explanation:

Diameter:

The diameter is always double the length of the radius.

Assuming d represents diameter:

d = 6.5(2)

d = 13

The diameter of the circle measures 13.

Circumference

The formula for circumference of a circle is dπ, where d is diameter and π is pi.

Now that we know the length of the diameter, we can find the circumference, or distance around the circle.

Assuming that C represents circumference

C = dπ
C = 13π
C = 13π or 40.84

The circumference measures 13π (exact value) or 40.84 (rounded to the nearest hundredth).

Area

The formula for area is A = ${r}^{2}$π. The radius measures 6.5, so we have enough information to solve for A

A = ${r}^{2}$π
A = ${6.5}^{2}$π
A = 42.25π or 132.73

The area is 42.25π $u n i t {s}^{2}$ or 132.73 $u n i t {s}^{2}$

Hopefully you understand some of the characteristics of circles now!