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A window is in the form of rectangle above which there is a semi circle. If the perimeter of window is p units, show that the window will allow maximum light, when radius of the semicircle is \( \large\frac{p}{\pi + 4} \) units.
cbse
class12
modelpaper
2012
sec-c
q24
math
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asked
Jan 24, 2013
by
thanvigandhi_1
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Jul 23, 2013
by
sreemathi.v
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A window is in the form of a rectangle above which there is a semicircle. If the perimeter of the window is P cm. Show that the window will allow the maximum possible light only when the radius of the semi circle is $\large\frac{p}{\pi+4}cm$
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A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the rectangle that will produce the largest area of the window.
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Show that volume of the greatest cylinder which can inscribed in a cone of height h and semi-vertical angle $ 30^{\circ} \: is \: \large\frac{4}{81} $$\: \pi h^3.$
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Jan 31, 2013
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Show that the rectangle of maximum area that can be inscribed in a circle is a square.
asked
Feb 11, 2013
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Show that the volume of the greatest cylinder that can be inscribed in a cone of height 'h' and semi-vertical angle \( \alpha \) is \( \large\frac{4}{27}\pi h^3\tan^2 \alpha \).
asked
Feb 4, 2013
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Show that semi vertical angle of right circular cone of given surface area and maximum volume is $ \sin^{-1} \bigg( \large\frac{1}{3} \bigg). $
asked
Feb 2, 2013
by
thanvigandhi_1
cbse
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