geometry: volume of cone

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If the radius of a cone is cut in half, the volume of the cone is multiplied by what number?

  • geometry: volume of cone -

    recall that volume of cone is given by
    V = pi*(r^2)*h/3
    where
    pi = 3.14 (constant)
    r = radius
    h = height
    if r becomes (1/2)r,
    V,new = pi*[(1/2)r]^2*h/3
    V,new = 1/4[pi*(r^2)*h/3]
    V,new = (1/4)V

    thus multiplied by 1/4.

    hope this helps~ :)

  • geometry: volume of cone -

    original volume = (1/3)π(r^2)h
    new volume = (1/3)π(r/2)^2 h = (1/3)π((r^2)/4)h

    so multiplied by 1/4

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