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4 April, 08:44

Discuss a more accurate method for approximating the volume of the spherical slab other than using just cylindrical slabs. Discuss in two to three sentences.

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  1. 4 April, 11:30
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    The volume of the a sphere can be approximated by the rotation of a circle

    Step-by-step explanation:

    The volume of a sphere can be found by rotating a circle which is the cross section of the sphere about the x axis that is rotating x² + y² = a²

    In the process of rotation, each cross section of the sphere generated will have a radius y from which the area of that cross section is π·y² = π· (a² - x²)

    Therefore, integrating from + a to - a gives the volume of the sphere as π*[a³ - x³/3]ᵃ₋ₐ which is equal to 4/3·π·r³ (the exact volume of a sphere).
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