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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