3. A football is in the shape of a solid obtained by rotating an ellipse = 1 about its major axis. An a² b² inflated NFL football averages 11.125 inches in length and 28.25 inches in center circumference. If the 4 volume of the ball istab, how much air does the football contain? (neglect material thickness) 3

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a.) Find the dimensions of the large rectangle that can be inscribed in the ellipse 9x^2 + 16y^2 = 144. The sides of the rectangle are parallel to the axes of the ellipse.  b.) the sum of the bases and altitude of an isosceles trapezoid is 36cm. Find the altitude if the area is to be a maximum. c.) A Norman window, consisting of a semicircle surmounting a rectangle, has a given perimeter. Find the radius of the semicircle to admit the most light. d.) Find the point the curve y= x^3 which is nearest the point (4,0). e.) the points (3,2) and (1,6) lie on the ellipse y^2 + 4x^2 = 40. Find a point on the ellipse so that the area of the triangle having these three points as vertices is maximum.

5. A highway overpass is in the shape of half an ellipse with the base 200 feet wide. The highway is 120 feet wide and the minimum clearance is 40 ft. Find the height of the overpass at its center.