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A window is in the form of a rectangle surmounted by a semicircular opening. The whole perimeter of the window is 30m. Find the dimension of the window so as to admit maximum light through the whole window

Posted by Nancy Agarwal 7 years, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Naveen Sharma 7 years, 3 months ago

Ans. Let 2r and x be the lenth and width of the window respectivily.

Then radius of semicircular portion is r.

Given : Perimeter of window = 10cm

Area of window is given by :

Differentiate w.r.t r, we get

To Find critical point, Put

Therefore , by second derivative test, the area is the maximum when

Now length of window =

Width of Window x =

0Thank You

ANSWER

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CBSE > Class 12 > Mathematics