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Provide notes on the calculation of the volume of solids by the method of slicing with example.
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Explanation of Solution
The volume of a solid of integrable cross-sectional area
Calculate the volume of a solid as follows:
- Sketch the solid and a typical cross section.
- Calculate the area of a typical cross-section.
- Calculate the limits of
integration . - Integrate the area of cross section to find the volume.
Example:
Consider the diagonal of the square runs from the parabola
Consider the solid lies between planes normal to the x axis at
The shape of the cross section is square.
Calculate the cross sectional area
Calculate the volume of the solid using the formula:
Substitute
Therefore, the volume of the solid is
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Chapter 6 Solutions
Thomas' Calculus (14th Edition)
- i need help pleasearrow_forwardQuestion 4 Find an equation of (a) The plane through the point (2, 0, 1) and perpendicular to the line x = y=2t, z=3+4t. 3t, (b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y. (c) The plane that contains the line x = parallel to the plane 5x + 2y + z = 1. 1+t, y2t, z = 43t and is (d) The plane that passes through the point (1,2,3) and contains the line x = 3t, y=1+t, and z = 2 – t. (e) The plane that contains the lines L₁ : x = 1 + t, y = 1 − t, z = = L2 x 2s, y = s, z = 2. 2t andarrow_forwardcan you explain why the correct answer is Aarrow_forward
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