# Diameter, Circumference, and area?

Dec 2, 2017

The diameter is $\frac{143}{8} \mathmr{and} 17.875$ inches, the circumference is $\frac{286957}{5110} = 56.15596868$, and the area is $\frac{620090}{2471} = 250.9469851$

#### Explanation:

To be honest, my geometry is not the best, but let’s give this a shot!

I’m not sure if $17 \frac{7}{8}$is the side length of the square, or the area of the square. I’m going to assume that it is the side length of the square.

For simplicity purposes, I’m going to convert $17 \frac{7}{8}$ to $\frac{143}{8}$

We can see from the illustration that the side length = to the diameter of the circle. So the diameter should be $\frac{143}{8} = 17.875$

The equation for the circumference is $2 \pi r$
Let’s find the radius first. Radius is half of the diameter so $r = \frac{d}{2} = \frac{\frac{143}{8}}{2} = \frac{143}{16}$
Now let’s input it into the circumference formula
$C = 2 \pi r = 2 \pi \left(\frac{143}{16}\right) = \frac{286957}{5110} = 56.15596868$

The equation of an area of a circle is $\pi {r}^{2}$
Since we know what r is, we can input that into this equation.
$A = \pi {r}^{2} = \pi {\left(\frac{143}{16}\right)}^{2} = \frac{620090}{2471} = 250.9469851$