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12 May, 08:43

Acorns height is six times greater than the measurement of the cones radius the volume of a cone is 401.92 inches^3 what are the cones dimensions? Use 3.14 for pi

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Answers (2)
  1. 12 May, 09:01
    0
    Answer: The cone's radius is 4 inches and it's height is 24 inches

    Step-by-step explanation: If the height is six times the radius, and the radius is r, then the height shall be 6 times r which equals 6r.

    The volume is also given as 401.92. If the volume of a cone is given as

    Volume = Pi x r^2 x (h/3)

    401.92 = 3.14 x r^2 x (6r/3)

    401.92 = 3.14 x r^2 x 2r

    By cross multiplication we now have

    401.92/3.14 = 2r^3

    128 = 2r^3

    128/2 = r^3

    64 = r^3

    Add the cube root sign to both sides of the equation

    4 = r

    Since the height is given as six times greater than the radius,

    Height = 6r

    Height = 6 x 4

    Height = 24

    Therefore the dimensions are,

    Radius = 4 inches

    Height = 24 inches
  2. 12 May, 09:12
    0
    radius = 4 inches

    height = 24 inches

    Step-by-step explanation:

    The formula of the volume of a cone is:

    V = (1/3) * pi * r^2 * h

    where V is the volume, r is the radius of the base and h is the height.

    We know that the height is 6 times greater than the base radius, so:

    h = 6*r

    If the volume is 401.92 in3, we can calculate the radius and the height of the cone:

    401.92 = (1/3) * 3.14 * r^2 * 6*r

    (1/3) * 3.14 * 6 * r^3 = 401.92

    r^3 = 401.92 / ((1/3) * 3.14 * 6) = 64

    r = 4 inches

    h = 6*r = 6*4 = 24 inches.
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