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Math - Please Help

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A right circular cone has a volume of 140 in^3. The height of the cone is the same length as the diameter of the base. Find the radius and height.

  • Math - Please Help -

    We know the formula for the Volume of a Right Circular Cone is given by
    V=(1/3)*pi*r^2*h
    V=140 in^3
    The height of the cone = diameter of the base. The diameter = 2 times the radius, so h = 2r
    The formula for Volume can now be written as
    V=(1/3)*pi*r^2*(2r)
    which simplifies to
    V=(2/3)*pi*r^3
    You plug in 140 in^3 for V and solve for r. Then you can plug the value you find for r into the equation h=2r

  • Math - Please Help -

    V = (1/3 π r^2 h , but h = 2r
    3V = π r^2 (2r) = 2π r^3
    420 = 2πr^3
    r^3 = 210/π
    r = (210/π)^(1/3) = 4.0584

    r = 4.0584
    h = 8.11683

    check:
    V = (1/3)π(4.0584)^2 (8.11683) = 139.9989.. , not bad

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