2. A cylindrical can with a bottom but no top will be constructed that will have a volume of 30 cm cube. Determine the dimensions of the can that will minimize the amount of material needed to construct the can. Answer: 47 r = 2.1216 h =2.1215 Solution:
3. A a piece of cardboard that is 50 cm by 20 cm are going to cut out the corners and fold up the sides to form a box. Determine the height of the box that will give a maximum volume. Answer: 48 h = 4.4018 h 50-2h 20-2h Solution:
h Answer: 49 4. A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12 meters of framing materials(perimeter) what are the dimensions of the window?. 2r r r = 1.6803, h = 1.6803 Hint: Solution:
5. A carpenter is building a rectangular shed with a fixed perimeter of 54ft. Find its dimensions. y x Answer: 50 x = 13.f ft, y = 13.5 ft, A=182.25 ft square Solution:
6. A goalpost is built with open end. The volume is 200 meter cubic. Find the dimensions of the goalpost so that the area is minimum. x Answer: 51 x y Hint: Solution:
REFERENCES Mohd Khanafiah Ismail, Wan Ainun Mior Othman, Mustafa Mamat (2015) Engineering Mathematics 2. Selangor : Oxford Fajar Sdn. Bhd. Martha T. Goshaw (2008) Concepts of Calculus with Applications. U.S.A : Pearson Education, Inc. Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey (2008) Calculus with Applications (9th Edition). U.S.A : Addison Wesley. Marvin L. Bittinger, David J. Ellenbogel, Scott A. Surgent (2012) Calculus and its Applications (10th Edition). U.S.A : Addison Wesley. 52
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