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Show that the triangle of maximum area that can be inscribed in a given circle.
is an equilateral triangle.
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Fine the dimensions of the rectangle of greatest area that can be inscribed in a
semicircle of radius r.
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The three sides of a trapezium are eual, each being 6 inch long. find the area
of the trpezium when it is maximum.
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A light house is located at A, 2 miles off-shore from the nearest point O on a
straight beach and a shop is located at B. the shop is located on the beach,
4 miles distant form O. If the house keeper can row at the rate of 4 miles per
hour, and walk at the rate of 6 mper hour, where should he plan to reach the
shore, so as to cover the distance to the shop in the eleast possible time?
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A running track of 440 meters is to ve laid out enclosing a football filed, the
shapre of which is a rectangle with a semicircle at each end. If the ares of the
rectangu;ar portion is to be maximum, find the length of its sides.
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Find the radius of the closed cylindrical can (right circular cylinder) which
encloses a given volume of 100 cubic can and has the minimum surface area.
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