Question
A window frame is shaped like a rectangle with an arch forming the top ( ie; a box with a semicircle on the top)
The vertical straight side is Y, the width at the base and at the widest part of the arch (Diam) is X.
I know that the perimeter is 4.
Find X if the area of the frame is at a maximum?
Joshi sir comment
perimeter = 4 so 2Y + X + πX/2 = 4
and area = XY + [π(X/2)2]/2
put Y from 1st equation to 2nd we get A = X[4-X{1+(π/2)}]/2 + πX2/8
now calculate dA/dX and then compare it to zero
X will be 8/(4+π)
Read 1 Solution.
PRATEEK PANDEY 12 year ago
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