376 CHAPTER 3 Polynomial and Rational Functions 94. Area of a Rectangle Find the value of x in the figure that will maximize the area of rectangle ABCD. Round to the nearest thousandth. y A 0 B D C(x, y) y = 9 – x2 x 95. Butane Gas Storage A storage tank for butane gas is to be built in the shape of a right circular cylinder of altitude 12 ft, with a half sphere attached to each end. If x represents the radius of each half sphere, what radius should be used to cause the volume of the tank to be 144pft3? 12 ft x 96. Volume of a Box A standard piece of notebook paper measuring 8.5 in. by 11 in. is to be made into a box with an open top by cutting equal-size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Use the table feature of a graphing calculator to do the following. Round to the nearest hundredth. (a) Find the maximum volume of the box. (b) Determine when the volume of the box will be greater than 40 in.3. 97. Floating Ball The polynomial function ƒ1x2 = p 3 x3 - 5px2 + 500pd 3 can be used to find the depth that a ball 10 cm in diameter sinks in water. The constant d is the density of the ball, where the density of water is 1. The smallest positive zero of ƒ1x2 equals the depth that the ball sinks. Approximate this depth for each material and interpret the results. (a) A wooden ball with d = 0.8 (to the nearest hundredth) (b) A solid aluminum ball with d = 2.7 (c) A spherical water balloon with d = 1 98. Floating Ball Refer to Exercise 97. If a ball has a 20-cm diameter, then the polynomial function becomes ƒ1x2 = p 3 x3 - 10px2 + 4000pd 3 . This function can be used to determine the depth that the ball sinks in water. Find the depth that this size ball sinks when d = 0.6. Round to the nearest hundredth.
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