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The volume of a cone is 54 pi cubic inches. The radius and height of the cone are both reduced by a factor of 3 to create a new cone. What is the volume of the new cone?

Is the volume of the new cone 18pi cu in

A. 2 pi cu inches
B. 6 pi cu inches
C. 9 pi cu inches
D. 18 pi cu inches

  • geometry - ,

    Is the answer 18 pi cu inches

  • geometry - ,

    V = (pi*r^2*h) / 3 = 54pi.

    Vn = (pi*(r/3)^2*(h/3)) / 3 = 54pi,
    Vn = (pi*(r^2/9)*(h/3)) / 3 = 54pi,
    Vn = (pi*r^2*(1/27)*h) / 3 = 54pi,
    We have divided the left side of our Eq by 27. Therefore , we must divide
    the rt. side by 27 also:

    Vn = (pi*r^2*(1/27)*h) / 3 = 2pi. =
    New volume = "A".

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