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November 9th, 2017, 02:42 PM   #1
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Related rates - inscribed

A rectangle is inscribed in a semicircle of a radius 5m. Estimate the increase in the area of the rectangle using differentials if the length of its base along the diameter is increased from 6m to 6 1/6 m ?
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November 9th, 2017, 07:39 PM   #2
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Show your work you lazy Canuck!!
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November 10th, 2017, 04:15 AM   #3
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A rectangle "inscribed in a circle" can't have its base "along the diameter". Your question makes no sense.
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November 10th, 2017, 04:45 AM   #4
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The problem states "inscribed in a semicircle", not "inscribed in a circle", so it does make sense.
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November 10th, 2017, 04:56 AM   #5
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Right. Thanks, I misread it.

Igorrrawr, set up a coordinate system with the origin at the center of the semicircle, the x-axis along its base. We can write the semi-circle as $y= \sqrt{25- x^2}$. The vertices of the rectangle on the semi-circle are of the form $\left(x, \sqrt{25- x^2}\right)$ and $\left(-x, \sqrt{25- x^2}\right)$ for some positive x. The area is given by $A= 2x\sqrt{25- x^2}$. Initially, the base is 6 so x= 3 and $A= 6\sqrt{25- 9}= 6(4)= 24$. Differentiate the formula for A to find dA in terms of x and dx, then set dx= 1/6.
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