Provide notes on the calculation of the volume of solids by the method of slicing with example.
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)