# circumfrence and area

• July 19th 2007, 07:59 PM
sanee66
circumfrence and area
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?
• July 19th 2007, 09:00 PM
earboth
Quote:

Originally Posted by sanee66
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

$c_N = 2 \pi R$

Now the radius of circle P is: $r = \frac{1}{2} R$

Now plug in this term into the formula to calculate the circumference:

$c_P = 2 \pi r = 2 \pi \left( \frac{1}{2} R \right) = \pi R$

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: $a = \pi ~r^2$

Plug in the value for r into this formula and you'll get:

$a_P = \pi \cdot 37.68^2 \approx 4460.3779...$