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| Math Central | Quandaries & Queries |
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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
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