More Applications of the Derivative Chapter 29 24. Find the height of the cone of minimum volume circumscribed about a sphere of radius 10.0 m (Fig. 29-55). 10.0 m Cone circumscribed FIGURE 29-55 about sphere. 25. Find the altitude of the cone of maximum volume that can be inscribed in a sphe radius 9.00 m Most Economical Dimensions of Containers 26. What should be the diameter of a can holding 1 L and requiring the least amount of metal if the can is open at the top? 27. A silo (Fig. 28-26) has a hemispherical roof, cylindrical sides, and circular floor, all made of steel. Find the dimensions for a silo having a volume of 755 m3 (including the dome that needs the least steel. Minimum Travel Time 28. A man in a rowboat at P (Fig. 29-56), 6.00 km from shore, desires to reach point Q on the shore at a straight-line distance of 10.0 km from his present position. If he can wals 4.00 km/h and row 3.00 km/h, at what point L should he land in order to reach Q in the shortest time? Shore L 6.00 km 10.0 km FIGURE 29-56 Find the fastest route from boat P to shore at Q. Beam Problems 29. The strength S of the beam in Fig. 29-38 is given by S Find x and y for the strongest rectangular beam that can be cut from a 45.0-cm-diam cylindrical log. kxy, where k is a const

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