SEARCH HOME
 Math Central Quandaries & Queries
 Question from al: Hi I cant work out the algebra. How does pir^2 = 1/4pid^2? Thanx

Hi Al,

The radius $r$ of a circle is half the diameter $d$ and thus

$\pi \; r^2 = \pi \left(\frac{d}{2}\right)^2 = \pi \left(\frac{d}{2}\right)\times \left(\frac{d}{2}\right)=\pi \left(\frac{d \times d}{2 \times 2}\right) = \pi \left(\frac{d^2}{4}\right) = \frac{\pi}{4} d^2 .$

I hope this helps,
Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.