SOLUTION: two circular cylinders have the same altitude. Find the ratio of their volumes if the radius of one cylinder is 5 times the diameter of the other.

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Question 717051: two circular cylinders have the same altitude. Find the ratio of their volumes if the radius of one cylinder is 5 times the diameter of the other.
Found 2 solutions by KMST, Alan3354:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a cylinder is calculated as the surface area of its base times the height.

CORRECTED CORRECTION:
This is what happens when you reach retirement age.
If the radius R of one cylinder is 5 times the diameter of the other,
Then R=5%2A%282r%29 --> R=10r
and the ratio of volumes will be 10%5E2=highlight%28100%29

OOPS! It was not 2 times! My previous solution below is the answer to the problem in my head, as I (mis)remembered it, not the answer to the problem as written above.
The two cylinders have height h and radii r and 2r (in the dictionary, the word radiuses is allowed as a plural, but spellchecker does not like it).
Their volumes will be
pi%2Ar%5E2%2Ah and pi%2A%282r%29%5E2%2Ah=pi%2A4r%5E2%2Ah
so the ratio of their volumes is
pi%2A4r%5E2%2Ah%2F%28pi%2Ar%5E2%2Ah%29=highlight%284%29 or 4:1 if you prefer to express it that way.
The larger cylinder has a volume that is 4 times the volume of the smaller one.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
two circular cylinders have the same altitude. Find the ratio of their volumes if the radius of one cylinder is 5 times the diameter of the other.
--------------------
r1 = 5d2 --> r1 = 10*r2
The larger radius is 10 times the smaller.
Volume is a function of the square of the radius
--> V1 = 100*V2