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The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is?
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The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-...
Volume of the Solid Bounded by Surfaces
The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 can be calculated using double integration in the xyz-coordinate system.
Setting up the Integral
To find the volume, we need to set up a triple integral where the limits of integration are determined by the intersection points of the surfaces and planes.
- The limits of integration for x will be from y^{2}-1 to 1-y^{2}.
- The limits of integration for y will be from -1 to 1.
- The limits of integration for z will be from 0 to 2.
Volume Calculation
The volume V of the solid can be calculated as:
V = ∫∫∫ dV
where dV = dx dy dz.
After setting up the triple integral and performing the calculations, the volume of the solid bounded by the given surfaces and planes is found to be approximately V = 2.67 units^3 (rounded off to 2 decimal places).
Therefore, the volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 is approximately 2.67 units^3.
The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 can be calculated using double integration in the xyz-coordinate system.
Setting up the Integral
To find the volume, we need to set up a triple integral where the limits of integration are determined by the intersection points of the surfaces and planes.
- The limits of integration for x will be from y^{2}-1 to 1-y^{2}.
- The limits of integration for y will be from -1 to 1.
- The limits of integration for z will be from 0 to 2.
Volume Calculation
The volume V of the solid can be calculated as:
V = ∫∫∫ dV
where dV = dx dy dz.
After setting up the triple integral and performing the calculations, the volume of the solid bounded by the given surfaces and planes is found to be approximately V = 2.67 units^3 (rounded off to 2 decimal places).
Therefore, the volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 is approximately 2.67 units^3.
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The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is?
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The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is?.
The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is?.
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