The exact circumference of the circle is: D. [tex]29\pi[/tex]
The formula for circumference of a circle is given as:
[tex]C = 2\pi r[/tex]
However, we are not given the radius so we need to solve for it.
We can see that there is a triangle inscribed within the circle whose hypotenuse spans from one side of the circle to the opposite side. The hypotenuse would be equivalent to the diameter of the circle.
So, we can solve for the hypotenuse using Pythagorean's Theorem which states:
[tex]a^2 + b^2 = c^2[/tex]
In this case:
The legs an and b would be 21 mm and 20 mm.
It becomes:
[tex]21^2 + 20^2 = c^2\\ 441 + 400 = c^2 \\841 = c^2 \\c = 29 \\[/tex]
Therefore the diameter is 29 mm.
Take half of it to get the radius.
[tex]r = 1/2(29) \\r = 14.5[/tex]
Plug in the radius to obtain your circumference.
[tex]C = 2\pi r \\C = 2\pi(14.5) \\C = 29\pi[/tex]
Thus, the circumference of the circle would be approximately 29pi.
