In figure below, R is the midpoint of NP. If the circumference of circle N is 75.36, what is the area of circle P?
Hello,
the circumference of circle N is calculated by
$\displaystyle c_N = 2 \pi R$
Now the radius of circle P is: $\displaystyle r = \frac{1}{2} R$
Now plug in this term into the formula to calculate the circumference:
$\displaystyle c_P = 2 \pi r = 2 \pi \left( \frac{1}{2} R \right) = \pi R$
That means the circumference of circle P is half as long as the circumference of circle N.
EDIT:
Thus r = 75.36 / 2 = 37.68.
The area of a circle is calculated by: $\displaystyle a = \pi ~r^2$
Plug in the value for r into this formula and you'll get:
$\displaystyle a_P = \pi \cdot 37.68^2 \approx 4460.3779...$