The diameter is twice the radius:

\(\displaystyle D=2(10)\)

\(\displaystyle D=20\)

The equation for circumference of a circle is as follows:

\(\displaystyle C=2 \pi r\)

Plug in the given values and solve for the radius:

\(\displaystyle 36\pi=2\pi r\)

Now we divide each side by \(\displaystyle 2\pi\):

\(\displaystyle 18=r\)

We know the equation for the circumference of a circle is \(\displaystyle C=2\pi r\). We also know that the the diameter is the twice the radius, so we can write \(\displaystyle C=D\pi\).

Plug in the given values and solve:

\(\displaystyle 25\pi=D\pi\)

\(\displaystyle 25=D\)

The diameter of a circle is twice the radius:

\(\displaystyle D=2r\)

Plug in the radius value:

\(\displaystyle D=2(9)\)

\(\displaystyle D=18\)

The radius is half of the diameter, or 11.

In order to solve this question, start by finding the radius.  Recall that the area of a circle is computed as:

\(\displaystyle A=\pi r^2\)

For our data, this is:

\(\displaystyle 144\pi = \pi r^2\)

Solving for \(\displaystyle r\), we get:

\(\displaystyle 144=r^2\) or \(\displaystyle r=12\)

Now, recall that the diameter is double the radius.  Thus, it is \(\displaystyle 24\).

Recall that the circumference formula is:

\(\displaystyle C=2\pi r\)

Now, for your data, this gives you:

\(\displaystyle 17=\pi r\)

You need to be careful, for some students get confused when they have to divide by \(\displaystyle \pi\).  However, just treat it like any other number or variable.  This means that you can solve for \(\displaystyle r\) and get:

\(\displaystyle r=\frac{17}{\pi}\)

Write the area formula of a circle.

\(\displaystyle A=\pi r^2\)

Substitute the area.

\(\displaystyle 30=\pi r^2\)

Divide by pi on both sides.

\(\displaystyle \frac{30}{\pi}=\frac{\pi r^2}{\pi}\)

\(\displaystyle r^2 = \frac{30}{\pi}\)

Square root both sides.

\(\displaystyle \sqrt{r^2} =\sqrt{ \frac{30}{\pi}}\)

\(\displaystyle r=\sqrt{ \frac{30}{\pi}}\)

The radius is:  \(\displaystyle \sqrt{\frac{30}{\pi}}\)

The diameter is double the radius.

The answer is:  \(\displaystyle 2\sqrt{\frac{30}{\pi}}\)

Write the formula for the area of a circle.

\(\displaystyle A=\pi r^2\)

Substitute the area into the equation.

\(\displaystyle 14\pi=\pi r^2\)

Divide by pi on both sides.

\(\displaystyle \frac{14\pi}{\pi}=\frac{\pi r^2}{\pi}\)

\(\displaystyle r^2 = 14\)

\(\displaystyle r=\sqrt{14}\)

The diameter is twice the radius. 

The answer is:  \(\displaystyle 2\sqrt{14}\)

There are three feet in one yard.

Using dimensional analysis, we can determine the given diameter in yards first.

\(\displaystyle 12 \textup{ ft}(\frac{1 \textup{ yd}}{3 \textup{ ft}}) = 4 \textup{ yds}\)

The radius is half the diameter.

The answer is:  \(\displaystyle 2 \textup{ yds}\)