Surfaces of cones

The diameter of the base of the cone is 24x cm.
The height of the cone is 16x cm.

The curved surface area of the cone is 2160pi cm^2.
The volume of the cone is V pi cm^3, where V is an integer.

What is the value of V. Answer is cm^2.

Thanks a lot.

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  1. πr√(r^2+h^2) = 2160π
    (12x)√(144x^2+256x^2) = 2160
    (12x)(20x) = 2160
    x^2 = 9
    x = 3

    so, the volume is

    π/3 r^2h
    = (π/3) (24*3)^2 (16*3)
    = 82944π

    V = 82944 cm^3

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  2. Steve's answer is incorrect.

    In the final stage, he said (24*3)^2.
    However, 24 is not the RADIUS of the cone's base. It is the DIAMETER.

    Therefore, you must halve 24.
    The final calculation should hence be:
    V = (π/3) (12*3)^2 (16*3)
    = 20736

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