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Consider a closed storage tank S with walls given by the curved surfaces x = y', z > 0 and r = 2 – y?, z > 0, floor at z = 0, and roof is part of the plane x + 2y + 2z = 6. (a) Sketch S, clearly labelling any intercepts. (b) Find the area of the roof of the tank. (c) Write down an expression for the volume of the tank as a triple integral.

Consider a closed storage tank S with walls given by the curved surfaces x = y', z > 0 and r = 2 – y?, z > 0, floor at z = 0, and roof is part of the plane x + 2y + 2z = 6. (a) Sketch S, clearly labelling any intercepts. (b) Find the area of the roof of the tank. (c) Write down an expression for the volume of the tank as a triple integral.

Advanced Engineering Mathematics
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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3. Consider a closed storage tank S with walls given by the curved surfaces x = y, z > 0 and a = 2 – y', z > 0, floor at z = :0, and roof is part of the plane x + 2y + 2z 6. (a) Sketch S, clearly labelling any intercepts. (b) Find the area of the roof of the tank. (c) Write down an expression for the volume of the tank as a triple integral. (d) Evaluate the integral in part (c) using the MATLAB symbolic toolbox.
Transcribed Image Text:3. Consider a closed storage tank S with walls given by the curved surfaces x = y, z > 0 and a = 2 – y', z > 0, floor at z = :0, and roof is part of the plane x + 2y + 2z 6. (a) Sketch S, clearly labelling any intercepts. (b) Find the area of the roof of the tank. (c) Write down an expression for the volume of the tank as a triple integral. (d) Evaluate the integral in part (c) using the MATLAB symbolic toolbox.
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