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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 37E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad29f6c2-22fc-44c8-9a71-d9083e24d581%2Feae352f6-ac30-4fce-88e8-7d7799663694%2Fdk6t4eg_processed.png&w=3840&q=75)
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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