Consider a closed storage tank S with walls given by the curved surfaces x = y^2; z ≥ 0 and x = 2-y^2; 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^2; z ≥ 0 and x = 2-y^2; 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.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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Consider a closed storage tank S with walls given by the curved surfaces
x = y^2; z ≥ 0 and x = 2-y^2; 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.
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