1 Answer

Andrew Flanagan · Answer 1 · 2023-11-14T06:29:33+0000

The area A of a circle is given by

$A=\pi r^2$

where Pi is 3.1416 and r is the radius. In our case, we get

$100\operatorname{mm}=\pi r^2$

and we need to find r. In this regard, if we move Pi to the left hand side we get

$(100)/(\pi)=r^2$

then, r is given by

$r=\sqrt[]{(100)/(\pi)}$

Now, the circunference C is given by

$C=2\pi\text{ r}$

then, by substituting our last result into this formula, we have

$C=2\pi\sqrt[]{(100)/(\pi)}$

since square root of 100 is 10, we get

$C=2\pi\frac{10}{\sqrt[]{\pi}}$

we can rewrite this result as

$\begin{gathered} C=\frac{2\pi*10}{\sqrt[]{\pi}} \\ C=\frac{2\sqrt[]{\pi\text{ }}\sqrt[]{\pi}*10}{\sqrt[]{\pi}} \end{gathered}$

and we can cancel out a square root of Pi. Then, we have

$C=2\sqrt[]{\pi}*10$

and the circunference is

$C=20\text{ }\sqrt[]{\pi}\text{ milimeters}$

Please log in or register to add a comment.