149 1.5 Applications and Modeling with Quadratic Equations 29. Manufacturing to Specifications A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area 8pft2. What should the radius of the circular top and bottom of the container be? (Hint: The surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and unrolled.) 30. Manufacturing to Specifications In Exercise 29, what radius would produce a container with a volume of p times the radius? (Hint: The volume is the area of the circular base times the height.) 31. Dimensions of a Square What is the length of the side of a square if its area and perimeter are numerically equal? 32. Dimensions of a Rectangle A rectangle has an area that is numerically twice its perimeter. If the length is twice the width, what are its dimensions? 33. Radius of a Can A can of Blue Runner Red Kidney Beans has surface area 371 cm2. Its height is 12 cm. What is the radius of the circular top? Round to the nearest hundredth. 34. Dimensions of a Cereal Box The volume of a 15-oz cereal box is 180.4 in.3. The length of the box is 3.2 in. less than the height, and its width is 2.3 in. Find the height and length of the box to the nearest tenth. 2.3 in. x x – 3.2 Solve each problem. See Example 2. 35. Height of a Dock A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 ft from the dock, the length of the rope from the boat to the dock is 3 ft longer than twice the height of the dock above the water. Find the height of the dock. 2h + 3 h Rope 12 ft 36. Height of a Kite Grady is flying a kite on 50 ft of string. Its vertical distance from his hand is 10 ft more than its horizontal distance from his hand. Assuming that the string is being held 5 ft above ground level, find its horizontal distance from Grady and its vertical distance from the ground. x + 10 x 50 ft 5 ft Kite
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