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22 December, 03:19

A cylinder has a radius of 6 inches and height of 3 and 3/4 inches. A sphere has a radius of 6 inches. What is the difference between the volume, to the nearest tenth of a cubic inch of the cylinder and sphere

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  1. 22 December, 03:31
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    Difference = 480.9 in³

    Step-by-step explanation:

    Given

    Cylinder;

    Height, h = 3¾ inches

    Radius, r₁ = 6 inches

    Sphere

    Radius, r₂ = 6 inches

    The volume of a cylinder is calculated as thus

    Volume, V₁ = πr₁²h

    The volume of a sphere is calculated as this

    Volume, V₂ = 4/3 πr₂³

    Calculating the volume of the cylinder

    V₁ = πr₁²h becomes

    V₁ = π * 6² * 3¾

    V₁ = π * 36 * 3¾

    V₁ = π * 36 * 15/4

    V₁ = π * 540/4

    V₁ = π * 135

    V₁ = 135π in³

    Calculating the volume of the sphere

    V₂ = 4/3 πr₂³ becomes

    V₂ = 4/3 * π * 6³

    V₂ = 4/3 * π * 216

    V₂ = 864/3 * π

    V₂ = 288π in³

    The difference between the volume is calculated as thus.

    Difference = V₂ - V₁

    Difference = 288π - 135π

    Difference = 153π

    Take π as 22/7

    Difference = 153 * 22/7

    Difference = 480.9 in³ (Approximated)
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