(b) How do you differentiate between Brittle and ductile materials? Which materials are preferred for design?
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.our firm has been asked to design a storage tank for liquid petroleum gas. The customer’s specifications call for a cylindrical tank with hemispherical ends, and the tank is to hold 8000 m3 of gas. The customer also wants to use the smallest amount of material possible in building the tank. What radius and height do you recommend for the cylindrical portion of the tank?
- A manufacturer is making cylindrical cans that hold 200 cm3. The dimensions of the can are not mandated, so to save manufacturing costs, the manufacturer wants to make the can that uses the least material. What are the dimensions, to the nearest three decimal places, of the can that has the smallest surface area?An industrial container is in the shape of a cylinder with hemispherical ends, as shown in the figure. The container must hold 1000 liters of fluid. Determine the radius r and length h that minimize the amount of material used in the construction of the tank.Your town has decided to drill a well to increase its water supply. As the town engineer, you have determined that a water tower will be necessary to provide the pressure needed for distribution, and you have designed the system shown here. The water is to be pumped from a 300-ft well through a vertical 4-in. pipe into the base of a cylindrical tank 20 ft in diameter and 25 ft high. The base of the tank will be 60 ft above ground. The pump is a 3-hp pump, rated at 1650 ft . lb/sec. To the nearest hour, how long will it take to fill the tank the first time? (Include the time it takes to fill the pipe.) Assume that water weighs 62.4 lb/ft3.
- 5. A closed cylindrical can is to hold 1 cubic meter of liquid. Assuming there is no waste or overlap, how should we choose the height and radius to minimize the amount of material needed to manufacture the can? (Assume that both dimensions do not exceed 1 meter.)A manufacturer needs to make a cylindrical can that will hold 1500 cubic centimeters of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction. Hint: Surface area of a cylinder =2πh +2πr^2 Volume of a cylinder =πr^2hYou are assigned to design a new drink Aluminium can with cylindrical shape for F&N Company. The can need to hold 1000 cm3 of drinks. How do you find the dimensions of surface area that will minimize the cost of the Aluminium material to manufacture the can?
- A cubical tank with a side = 12 m is full of water. Calculate the work required to pump the water through an opening at the top of the tank. Integrate by hand.1. Angelo, who is in a rowboat 2 kilometers from a straight shoreline wishes to go back to his house, which is on the shoreline and 6 kilometers from the point on the shoreline nearest Angelo. If he can row at 6 kph and run at 10 kph, how should he proceed in order to get to his house in the least amount of time?2. A closed box with a square base is to have a volume of 2000 cm3. The material for the top and bottom of the box costs P30 per square centimeter and the material for the sides cost P15 per square centimeter. Find the dimensions of the box so that the total cost of material is the least possible and all its dimensions do not exceed 20 cm.3. Find the radius and height of the right circular cylinder of largest volume that can be inscribed in a right circular cone with radius 4 cm and height 3 cm.4. An offshore oil well located at a point W that is 5 km from the closest point A on a straight shoreline. Oil is to be piped from W to a shore point B that is 8 km from A by piping it…You want to produce a cylindrical water container with a capacity of 350mL. What dimensions will minimize the amount of material required for the container?