SOLUTION: A pool with a volume of 1000 gallons requires a cover that is 250 sq. ft. What size cover is appropriate for a similarly-shaped pool that holds 3375 gallons?

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Question 1065354: A pool with a volume of 1000 gallons requires a cover that is 250 sq. ft. What size cover is appropriate for a similarly-shaped pool that holds 3375 gallons?
Found 2 solutions by KMST, josmiceli:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
When you "scale up" (or down) a shape,
to a similar shape where all dimension measurements
are changes by a factor k ,
the length ratio is k for all lengths,
the surface area ratio is k%5E2 for al surfaces,
and the volume ratio is k%5E3 for the one and only volume.
In this case,
k%5E3=3375%2F1000=15%5E3%2F10%5E3=%2815%2F10%29%5E3 ,
so k=15%2F10 and k%5E2=%2815%2F10%29%5E2=15%5E2%2F10%5E2=225%2F100 .
Applying that factor to 250 square feet,
we find the size (in square feet) of the larger pool to be
250%2A%28225%2F100%29=250%2A226%2F100=562.5

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think the covers would be p[roportional to
the squares of cube roots of the volumes of the pools
Since gallons are a measure of volume, I
think this will give a ratio of areas:
+%28root%28+3%2C+1000+%29%29%5E2+%2F+%28root%28+3%2C+3375+%29%29%5E2+=+10%5E2+%2F+15%5E2+
+10%5E2+%2F+15%5E2+=+100+%2F+225+
+100+%2F+225+=+4+%2F+9+
+4%2F9+=+250+%2F+x+
+4x+=+250%2A9+
+4x+=+2250+
+x+=+562.5+
The cover for the 3375 gal pool would be 562.5 ft2
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DEFINITELY get another opinion on this.
I am pretty much winging it.