The height of one right circular cylinder is 7 centimeters and its radius is 2 centimeters. The height of the second right circular cylinder

The height of one right circular cylinder is 7 centimeters and its radius is 2 centimeters. The height of the second right circular cylinder is 28 centimeters and its radius is also 2 centimeters. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder? A. 4:1 B. 5:1 C. 10:1 D. 25:1

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  1. Answer:  Choice A)  4:1

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    Explanation:

    The volume of a cylinder formula is

    V = pi*r^2*h

    where r is the radius and h is the height.

    —————

    For the first cylinder, we have r = 2 and h = 7. This leads us to…

    V = pi*r^2*h

    V = pi*2^2*7

    V = pi*4*7

    V = pi*28

    V = 28pi

    This is the exact volume in terms of pi.

    —————

    Repeat those steps for the other cylinder (r = 2 and h = 28)

    V = pi*r^2*h

    V = pi*2^2*28

    V = pi*4*28

    V = 112pi

    —————

    To recap so far, we have these two cylinder volumes:

    • Cylinder A = 28pi
    • Cylinder B = 112pi

    We see that cylinder B has the larger volume (since 112 > 28).

    The ratio of the volumes from larger to smaller is 112pi : 28pi

    Divide both parts by pi to have those terms cancel and we get the ratio 112:28

    Lastly, we divide each part by the GCF 28

    112/28 = 4

    28/28 = 1

    Therefore, the ratio 112:28 fully reduces to 4:1 which makes the final answer choice A.

    The larger volume is 4 times that of the smaller volume.

    —————-

    A fairly quick way to see why we get this ratio is to notice the smaller height h = 7 jumps to the larger height h = 28 by a factor of 4.

    In other words,

    larger height = 4*(smaller height)

    28 = 4*7

    The fact that the radius is kept the same at r = 2 won’t have an effect on the volume ratio. These parts effectively cancel out.

    So this jump of “times 4” directly connects to the ratio 4:1

    We multiplied the height by 4, so the volume is also multiplied by 4 (when going from the smaller cylinder to the larger one).

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