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8 January, 18:40

A cone has a volume of 108 pi and a base diameter of 12. What is the height of the cone?

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  1. 8 January, 19:47
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    h = 9 units of length

    Step-by-step explanation:

    Volume of a circular right cone is:

    V (c) = (1/3) * Area of the circular base * h

    Where h is the height of the cone, then

    V (c) = (1/3) * π * r² * h

    And we have that V (c) = 108*π

    Then:

    108 * π = (1/3) * π * r² * h (1)

    We know diameter of the circular base is 12 units, according to that

    r = d/2 ⇒ r = 12/2 r = 6 units

    Then:

    108 * π [ cubic units ] = (1/3) * π * (6) ² * h [square units] [ units of length]

    When simplifying we have to take into account that in order to keep last equation h needs to have units of length

    Therefore:

    108 = (1/3) * 36 * h

    h = (108 * 3) / 36

    h = 9 units of length
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