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  3. Volume by cross sections is a method of calculating the volume of a three-dimensional object by slicing it into thin cross sections and summing the volumes of these slices. This method is commonly used in calculus to find the volume of complex shapes that may not have a simple formula for finding volume.
    andymath.com/volume-by-cross-sections-calculus/
    To find the volume of a solid with known cross-sections we can use the formula: V = int_a^b A (x) dx V = ∫ ab A(x) dx where y=A (x) y = A(x) is a function for the area of a cross-section (some two-dimensional shape) perpendicular to the x-axis on the closed interval [a,b] [a,b] and dx dx represents its thickness.
    library.fiveable.me/ap-calc/unit-8/volumes-with-cros…
    Volumes with Known Cross Sections If we know the formula for the area of a cross section, we can find the volume of the solid having this cross section with the help of the definite integral. If the cross section is perpendicular to the x‐axis and itʼs area is a function of x, say A(x), then the volume, V, of the solid on [ a, b ] is given by
    wl.apsva.us/wp-content/uploads/sites/38/2017/02/7…
     
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      WEBJun 18, 2024 · To find the volume of a solid with known cross-sections we can use the formula: where y=A (x) y = A(x) is a function for the area of a cross-section (some two-dimensional shape) perpendicular to the x-axis …

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      WEBOct 22, 2018 · Determine the volume of a solid by integrating a cross-section (the slicing method). Find the volume of a solid of revolution using the disk method. Find the volume of a solid of revolution with a cavity …

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      WEBDec 21, 2020 · Example \(\PageIndex{2}\): Finding volume using the Disk Method. Find the volume of the solid formed by revolving the curve \(y=1/x\), from \(x=1\) to \(x=2\), around the \(x\)-axis. Solution. A sketch can help …

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      WEBDetermine the volume of a solid by integrating a cross-section (the slicing method). Find the volume of a solid of revolution using the disk method. Find the volume of a solid of revolution with a cavity using the washer …

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