A hemispherical tank, placed so that the top is a circular region of radius 6 ft, is filledwith water to a depth of 4 ft. Find the work done in pumping the water to the top ofthe tank. (Choose the positive x axis downward and take the origin at the top of thetank, Draw an illustration with proper labelling)

Answered: Image /qna-images/answer/02852973-3b09-4734-8822-7a5c473ecd83.jpg

Answered: A hemispherical tank, placed so that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The fuel tank on a truck has trapezoidal cross sections with the dimensions (in feet) shown in the figure. Assume that the engine is approximately 3 feet above the top of the fuel tank and that diesel fuel weighs approximately 53.1 pounds per cubic foot. Find the work done by the fuel pump in raising a full tank of fuel to the level of the engine.
2. A cylindrical tank contains oil (use density as p in lb/ ft'). The radius of the tank is 3 feet, the length is 12 feet and oil enters and leaves the tank through an opening at the top. The tank is initially full of oil. Use the sketch below and complete each step below to find the work done in pumping all of the oil out of the opening at the top of the tank. You must use the axis provided. No calculators. (a) Find and expression for the volume of a single representative "slab" of oil that will move out of the tank. (b) Find the expression for the distance any single representative "slab" of oil must move to get out of the tank. (c) Find the expression for the force of a single representative "slab" of oil. (d) Set up (BUT DO NOT SOLVE), the Reimann sum that approximates the total work done in pumping all of the oil out of the tank.
A window frame must be built using exactly 12 metres of framing material. The window is in the shape of a semicircle of radius r on top of a rectangle of height h and width w. Determine the values of the height and width[in metres to the nearest centimetre] that will allow the most light in through the window.
Estimate the maximum volume of a conical pile of road salt that can be stored on an area in the shape of an equilateral triangle 150[ft] on a side. You must consider the angle of repose for the salt. Assumptions must be clearly identified. Figures are required.
A 10cm diameter disk emits light uniformly from its surface. 20 cm from this disk, along its axis, is a 7.0cm diameter opaque black disk; the faces of the two disks are parallel. 20 cm beyond the black disk is a white viewing screen. The lighted disk illuminates the screen, but there’s a shadow in the center due to the black disk. What is the diameter of the completely dark part of this shadow?

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