Format: Font Style: Calibri (Body) Font Size: 10 Line and Paragraph Spacing: 1.0 No Spacing Note: Problem numbering is based on the “Designated Problem #” excel tab. Maxima and Minima CE Board Nov 2000 35. A closed cylindrical tank having a volume of 71.57 𝑚3 is to be constructed, if the surface area is to be a minimum, what is the required diameter of the tank? a) 4 m b) 5.5 m c) 5 m d) 4.5 m Maxima and Minima CE Board Nov 2002 36. Suppose that x years after founding in 1975, a certain employee of a membership of 𝑓(𝑥) = 100(2𝑥 3 − 45𝑥 2 + 264𝑥), at what time between 1975 and 1989 was the membership smallest? a) 1983 b) 1985 c) 1984 d) 1986 Maxima and Minima CE Board Nov 2003 37. The sum of two numbers is C. the product of one of the cubes of the other is to be a maximum. Determine one of the numbers? a) 3C/4 b) 3C/8 c) 3C/2 d) 3C/7 Maxima and Minima CE Board May 2004 38. Triangle ABC have sides measuring AB = 7 m, BC = 5 m, and AC = 9 m. What is the width of the largest rectangle that can be inscribed in it, with the longer side of the rectangle along the 9-m side. a) 2.475 b) 1.514 c) 1.934 d) 4.5 Maxima and Minima CE Board Nov 2004 39. A right circular cylinder of a radius r and height h is inscribed in a right triangle cone of radius 6 m and height 12 m. 39.1. Determine the radius of the cylinder such that its volume is maximum. a) 2 m b) 4 m c) 3 m d) 5 m 39.2. Determine the maximum volume of the cylinder. a) 145.72 𝑚3 b) 321.12 𝑚3 c) 225.31 𝑚3 d) 201.06 𝑚3 39.3. Determine the height of a cylinder such that its lateral area is maximum. a) 10 m b) 8 m c) 6 m d) 4 m Maxima and Minima CE Board Nov 2004 40. A right circular cone has a base diameter of 24 cm. The maximum area of parabola segment that can be cut from this phone from this phone 207.8 𝑐𝑚2 . 40.1. Determine the base width of parabola. a) 22.32 cm b) 18.54 cm c) 15.63 cm d) 20.78 cm 40.2. Determine the altitude of the parabola. a) 14 cm b) 18 cm c) 15 cm d) 16 cm 40.3. Determine the altitude of the cone. a) 20 cm b) 14 cm c) 16 cm d) 18 cm Maxima and Minima CE Board May 2005 41. A corner lot, triangular in shape, has perpendicular sides measuring 120 m and 160 m, respectively. It is required to construct the largest rectangular building with sides parallel to the street. 41.1. What is the largest area of the building? a) 6,500 𝑚2 b) 7,200 𝑚2 c) 5,300 𝑚2 d) 4,800 𝑚2 41.2. What is the perimeter that encloses the building? a) 310 m b) 360 m c) 280 m d) 330 m 41.3. What is the cost of a three-storey building that can be constructed if it cost P5,000 per square meter per floor area? a) P93M b) P72M c) P85M d) P76M Maxima and Minima CE Board May 2006 42. The sides of a triangle sides are 9.61 m, 4.25 m and 8.62 m. Find the width of the largest rectangle that can be inscribed in the triangle with one side along the 9.61-m side. a) 4.81 m b) 1.91 m c) 3.51 m d) 2.71 m Maxima and Minima CE Board Nov 2015 43. An open top box with a square bottom and rectangular sides is to have a volume of 864 cu. Inches. Find the dimensions that require the minimum account of material. Hint: The amount of material needed for box is equal to the surface area. a) 12 in x 6 in b) 8 in x 13.5 in c) 14 in x 4.4 in d) 10 in x 8.6 in Maxima and Minima CE Board Nov 2016 44. A rectangular field bounded on one side by a building is to be fenced the other three sides. If 980 m of fence is to be used, find the dimension dimensions of the largest field that can be fenced in a) 280 m x 420 m b) 220 m x 540 m c) 245 m x 490 m d) 200 m x 580 m Maxima and Minima CE Board Nov 2017 45. A closed cylindrical container has a volume of 1000 𝑓𝑡 3 . If the lateral area cost P25 per square foot and the top and bottom cost P20 per square foot. Determine the minimum cost. a) P13,563.20 b) P12,847.50 c) P10,963.60 d) P11,254.70 Maxima and Minima CE Board Nov 2018 46. A farmer owns a square field measuring exactly 2261 m on each side. 1898 m from one corner and 1009 m from an adjacent corner stands Mahogany tree. A neighbor offered to purchase a triangular portion of the field stipulating that a fence should be erected in a straight line from one side of the field to an adjacent side so that the Mahogany tree was part of the fence. The farmer accepted the side so that the Mahogany tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was a minimum area. What was the area of the field the neighbor received and long was the fence? a) A = 950,160 and L = 2,122 b) A = 939,120 and L = 2,018 c) A = 971,325and L = 2,236 d) A = 946,350 and L = 2,495