The cylinders are similar. the volume of the larger cylinder is 40,635 cubic centimeters. what is the volume of the smaller cylinder?

1505 cubic centimeters

Step-by-step explanation:

Lengths are related by scale factor "k"

Volumes are related by scale factor "k^3"

From large to small:

What multiplied by 18, gives us 6? We can write:

18(k)=6

k = 6/18 = 1/3

So scale factor is 1/3

Now in terms of volume, the larger is given as 40, 635, so we can set up:

40,635 * k^3 = smaller volume

we know k = 1/3, so

40,635 * (1/3)^3 = smaller volume

Thus, smaller volume = 40,635 * (1/3)^3 = 1505

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