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[Solved] Circles

 
Circles & Cylinders
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June 15, 2021 3:02 pm
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Staff 
(@armor)
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A circular manhole is covered by a circular cover which has a diameter of 32 inches. If the manhole has a diameter of 30 inches, how much greater than the area of the manhole is the area of the cover, in square inches?

A) 21          B) 417          C) 241          D) 311          E) 1241

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June 15, 2021 3:03 pm
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Staff 
(@armor)
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Knowing the diameter of a circle is enough to determine its area, since \small a=\Pi r^2,  and \small r, the radius, is half the diameter. The radius of the cover is 

\small \frac{1}{2}(32)=16,  so the cover has an area of   \small \Pi (16)^2,  or  \small 256\Pi.

The manhole has a radius of   \small \frac{1}{2}(30),  or   \small 15,  so its area is \small \Pi (15)^2,  or  \small 225\Pi . 

So the area of the cover is   \small 256\Pi -225\Pi  or  \small 31\Pi  square inches greater than the area of the manhole.

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