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A sphere with a diameter of 24 inches is reshaped into a cone with a radius of 32 inches. If all the material is used, what is the height of the cone?

  • geometry -

    sphere: radius = s
    cone: radius c, height h

    4π/3 s^3 = π/3 c^2 h
    4s^3 = c^2 h
    4(12^3) = (32^2)h
    h = 4*4^3*3^3/2^10 = 3^3/2^2 = 27/4 = 6.75

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