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Math Help - Right Circular Cone

  1. #1
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    Right Circular Cone

    Water is poured into a container in the shape of a right circular cone with radius 4 feet and a height of 16 feet. Express the volume V of the water in the cone as a function of the height h of the water.

    HINT GIVEN:

    The volume V of a cone of radius r and height h is V = (1/3)(pi)(r^2)(h).

    NOTE: Since the radius is 4 feet, does it mean the diameter of the cone is 8 feet?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    Water is poured into a container in the shape of a right circular cone with radius 4 feet and a height of 16 feet. Express the volume V of the water in the cone as a function of the height h of the water.

    HINT GIVEN:

    The volume V of a cone of radius r and height h is V = (1/3)(pi)(r^2)(h).
    As the radius of the cone is 4 ft, and height is 16 ft, when the cone is filled
    to a height of h ft, the radius of the surface of the liquid is h/4 ft (as the
    filled part of the cone is similar to the whole cone the radius to height ratio
    is the same as that for the whole cone). So r=h/4, hence the volume:

    V=(1/3) pi r^2 h = (1/3) pi (h/4)^2 h= (1/48) pi h^3.

    NOTE: Since the radius is 4 feet, does it mean the diameter of the cone is 8 feet?
    yes

    RonL
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  3. #3
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    ok

    I get it now thanks to you.

    Thanks!
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