PLease solve and show full work. 37. Maximum Volume A package to be sent by a postalservice can have a maximum combined length and girth(perimeter of a cross section) of 108 inches. (a) Find thedimensions of the package of maximum volume thatcan be sent when the cross section is square (see figure).(b) What are the dimensions of a cylindrical package ofmaximum volume? (The cross section is circular.)

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Answered: Maximum Volume A package to be sent by…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter63: Volumes Of Pyramids And Cones

Section: Chapter Questions

Problem 16A: A piece in the shape of a pyramid with a regular octagon (eight sided) base is machined from a solid...

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A piece in the shape of a pyramid with a regular octagon (eight sided) base is machined from a solid block of bronze. Each side of the octagon base is 9.36 inches long. The height of the piece is 7.08 inches. The octagon base area 4.829, where s is the length of a side of the octagon. a. Determine the volume of the piece. Round the answer to the nearest cubic inch. b. Determine the weight of the piece. Round the answer to the nearest pound. Note: One cubic foot of the bronze used weighs 547.9 pounds per cubic foot.
A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispheric dome. The metal in the dome cost 1.7 times as much as the concrete (per unit of surface area). If the volume of the silo is 850 m³, what are the dimensions of the silo (radius and height of the cylindrical tower) that minimize the cost of the materials. Assume the silo has no floor and no flat ceiling under the dome. What is the radius of the cylindrical base (and the hemispherical dome) - rounded to the nearest tenth? Thanks.
A cylindrical can without a top is made to contain 10,000 cubic cm of liquid. Find the dimensions that minimize the cost of the metal to make the can.
minimum dimensions of a cylinder that can hold 1.5 liters of liquid?
4.6 optimization #28 a cylindrical container with no top is to be constructed to hold a fixed volume V0 of liquid. the cost of the material used for bottom is $0.50/in2 and cost of the material used for the curved lateral side is $0.30/in2 . use calculus to find radius (in terms of V0) of the leaset esxpensive container.
4. A fruit company is redesigning their packaging and must know optimal dimensions forits pineapple cans. Each cylindrical can should hold 21 cm^3 of pineapple preserves. The cost of materialsis such that the top and bottom of the can cost $0.03/cm^2 and the side costs $0.045/cm^2. What radiusand height of the can allow the company to minimize packaging cost? Round to three decimal places.
A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.7 times as much as the concrete (per unit of surface area). If the volume of the silo is 850 m3, what are the dimensions of the silo (radius and height of the cylindrical tower) that minimize the cost of the materials? Assume the silo has no floor and no flat ceiling under the dome.
A closed rectangular box is to have volume V cm3. The cost of the material used in the box is a cents/cm2 for top and bottom, b cents/cm2 for front and back, and c cents/cm2 for the remaining sides. What dimensions minimize the total cost of materials?
10. Ram a farmer, managed to grow shaped-watermelons inside glass cases ofdifferent shapes. The shapes he used were: a perfect cube, hemi-spherical, cuboid,cylindrical along with the normal spherical shaped watermelons. Thickness of the skinwas same for all the shapes. Each of the glass cases was so designed that the totalvolume and the weight of the all the water-melons would be equal irrespective of theshape. A customer wants to buy water-melon for making juice, for which the skin of the water-melon has to be peeled off, and therefore is a waste. Which shape should the customer buy?
A cylindrical can is to be made to hold 1 litre of oil. Find the dimensions which will minimize the cost of the metal to make the can. Answer:Height 10.84 cm, radius of the base = 5.42 cm = and material for the surface =37 square cm, nearly
A rectangular field having an area of 2500m2 is to be enclosed by a fence, andtwo additional fence is to be used to divide the field into three. the cost of the additionalfence to divide the field is 15 dollars per running meter, and the fence along the sidescosts 20 dollars per running meter. Determine the dimensions of the field so that thetotal cost of the fencing material is least.
A rectangular area of 28,000 ft2is to be fenced off. Twotypes of fencing material are being considered: Metal fencing whichcosts $2 per ft and Wooden fencing which costs $5 per foot. You willbe finding the dimensions (length and width) and the minimum totalcost for fencing the area for three different scenarios. In each case youshould find the exact value of both dimensions and an approximationto the nearest foot, as well as the total cost for fencing the area (to thenearest dollar). Find the minimum cost for fencing the rectangular area if metal fencing is used for all four sides. What would be the length and widthof this rectangle (exact value and rounded to the nearest foot)?

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