ace canning company is redesigning its product. The New cans will have twice the radius, but the same height of the original cans. Which statement is true about the volume of the new cans compared to the volume of the original cans? Show your work

A. The volume of the new and original cans will be equal

b. The volume of the new cans will be twice the volume of the original cans

c. The volume of the new cans will be four times the volume of the original cans

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  1. the volume is the base area times the height
    recall that area grows as the square of the linear scale factor (2)
    thus, the base area grows by a factor of 2^2 = 4

    since the height remains the same, and the new radius is twice the old radius, the new volume also grows by a factor of 4.

    To show this, look at the ratio of volumes (new/old):
    (π(2r)^2 h)/(πr^2 h) = (4πr^2h)/(πr^2h) = 4

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