SOLUTION: these two cylinders are similar. the ratio of their volumes is 8:27. the height of cylinder A is 12cm. find the height of cylinder B.

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Question 1044254: these two cylinders are similar.
the ratio of their volumes is 8:27.
the height of cylinder A is 12cm.
find the height of cylinder B.

Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
these two cylinders are similar.
the ratio of their volumes is 8:27.
the height of cylinder A is 12cm.
find the height of cylinder B.
:
Va%2FVb = 8%2F27
cross multiply
27Va = 8Vb
Va = 8%2F27Vb
let h = the height of cylinder B
pi%2Ar%5E2%2A12 = 8%2F27(pi%2Ar%5E2%2Ah)
divide both sides by pi%2Ar%5E2
12 = 8%2F27h
h = 27%2F8(12)
h = 40.5 cm

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
these two cylinders are similar.
the ratio of their volumes is 8:27.
the height of cylinder A is 12cm.
find the height of cylinder B.
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The condition does't say whether A is the larger or the smaller cylinder.
I will assume that A is the smaller cylinder.

Since the cylinders are similar and since the ratio of their volumes is 8%2F27,
the ratio of their linear dimensions/measures is root%283%2C+8%2F27%29 = 2%2F3  (similarity coefficient).

Next, since the height of the smaller cylinder is 12 cm, then the height of the larger cylinder is 12%2A%283%2F2%29 = 18 cm.