The information about the radius is unnecessary to the problem. The equation of the circumference is:

$\displaystyle C=d\pi$

$\displaystyle \pi \approx 3.14$

$\displaystyle C=3.14d$

Therefore, the circumference is $\displaystyle 3.14$ times larger than the diameter, and the ratio of the diameter to the circumference is:

$\displaystyle 1:3.14$

The information about the radius is unnecessary to the problem. The equation of the circumference is:

$\displaystyle C=d\pi$

$\displaystyle \pi \approx 3.14$

$\displaystyle C=3.14d$

Therefore, the circumference is $\displaystyle 3.14$ times larger than the diameter, and the ratio of the diameter to the circumference is:

$\displaystyle 1:3.14$

The area of a circle can be calculated as $\displaystyle Area=\pi r^2$ where $\displaystyle r$  is the radius of the circle, and $\displaystyle \pi$ is approximately $\displaystyle 3.14$.

 $\displaystyle Area=\pi r^2\Rightarrow r^2=\frac{Area}{\pi}$

$\displaystyle \Rightarrow r=\sqrt{\frac{Area}{\pi}}=\sqrt{\frac{25 \pi}{\pi}}=\sqrt{25}\Rightarrow r=5$

To find the diameter, multiply the radius by $\displaystyle 2$:

$\displaystyle d=2r=2\times 5=10$

If the area of a circle is equal to $\displaystyle 36\pi$, then the radius is equal to $\displaystyle 6$. 

This is because the equation for the area of a circle is $\displaystyle \pi r^{2}$.

Thus, $\displaystyle \pi r^{2}=36 \pi$.

$\displaystyle r^{2}=36$

$\displaystyle r=6$

Then the diameter is 12.

The circumference can be calculated as $\displaystyle C=2\pi r=\pi d$, where $\displaystyle r$ is the radius of the circle and $\displaystyle d$ is the diameter of the circle.

$\displaystyle C=2\pi r=\pi d$

$\displaystyle d = \frac{C}{\pi }=\frac{14\pi }{\pi }=14$

If the value of a radius is $\displaystyle x^{2}-^{\sqrt{x+4}}+2$, and the value of $\displaystyle x=3$, then the radius will be equal to:

$\displaystyle 3^{2}-^{\sqrt{3+4}}+2$

$\displaystyle 9-^{\sqrt{7}}+2$

$\displaystyle 11-^{\sqrt{7}$

Given that the diameter is twice that of the radius, the diameter will be equal to:

$\displaystyle 2(11-^{\sqrt{7}})$

This is equal to:

$\displaystyle 22-^{2\sqrt{7}$

The median is the middle number in a set when that set is ordered smalles to largest. 

When $\displaystyle 6, 9, 5, 4, 3$ is ordered smallest to largest, we get $\displaystyle 3, 4, 5, 6, 9$

Here, the median would be $\displaystyle 5$. 

Given that a diameter is twice the radius, the diamater would be $\displaystyle 10$ (twice the value of $\displaystyle 5$). 

You have a circular lens with a circumference of $\displaystyle 16.67 \pi in$, find the diameter of the lens.

Begin with the circumference of a circle formula.

$\displaystyle C=2 \pi r$

Now, we know that 

$\displaystyle 2r=d$

Because our radius is half of our diameter.

So, we can change our original formula to be:

$\displaystyle C= \pi d$

Now, we can see that all we need to do is divide our circumference by pi to get our diameter.

$\displaystyle \frac{C}{\pi}=d$

Now plug in our known and solve:

$\displaystyle \frac{16.67 \pi in}{\pi}=d=16.67 in$

So our answer is 16.67inches

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be $\displaystyle 169 \pi m^2$.

What is the diameter of the crater?

To solve this, we need to recall the formula for the area of a circle.

$\displaystyle A=\pi r^2$

Now, we know A, so we just need to plug in and solve for r!

$\displaystyle 169 \pi m^2=\pi r ^2$

Begin by dividing out the pi

$\displaystyle 169m^2=r^2$

Then, square root both sides.

$\displaystyle r=\sqrt{169m^2}=13m$

Now, recall that diameter is just twice the radius.

$\displaystyle d=2r=13m (2)=26m$