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Unformatted text preview: to form a cone. ²ind the magnitude of φ so that the volume of the cone is maximized. 6. Twenty feet of wire are to be used to form two ±gures. In each of the following cases, how much should be used for each ±gure so that the total enclosed area is a maximum? a) equilateral triangle and square b) square and regular pentagon c) regular pentagon and hexagon d) regular hexagon and circle (Hint: The area of a regular polygon with n sides of length x is A = n 4 cot( π n ) x 2 .) What can you conclude from this pattern? 7. Two hallways meet at right angles. Their widths are a and b as indicated in the picture. What is the greatest length of a ladder which can be carried horizontally around the corner? a b 8. a) Find the closest point on the graph of f ( x ) = x 2 to the point ( a, b ). b) Show that the line connecting (0 , b ) to the closest point is normal to the graph at that point....
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