SOLUTION: the ratio of the sides of two cubes is 2:3 and the different of their voloumes is 152. find the side of the bigger cube.

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Question 606143: the ratio of the sides of two cubes is 2:3 and the different of their voloumes is 152. find the side of the bigger cube.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the volume of the smaller cube = +V%5B1%5D+
Let the volume of the bigger cube = +V%5B2%5D+
Let the side of the smaller cube = +s%5B1%5D+
Let the side of the bigger cube = +s%5B2%5D+
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given:
+s%5B1%5D%2Fs%5B2%5D+=+2%2F3+
(1) +s%5B1%5D+=+%282%2F3%29%2As%5B2%5D+
(2) +V%5B2%5D+-+V%5B1%5D+=+152+
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The formulas for volume are
+V%5B1%5D+=+s%5B1%5D%5E3+
+V%5B2%5D+=+s%5B2%5D%5E3+
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Substituting into (2),
(2) +V%5B2%5D+-+V%5B1%5D+=+152+
(2) +s%5B2%5D%5E3+-+s%5B1%5D%5E3+=+152+
Substitue (1) into (2)
(2) +s%5B2%5D%5E3+-+%28%282%2F3%29%2As%5B2%5D%29%5E3+=+152+
(2) +s%5B2%5D%5E3+-+%288%2F27%29%2As%5B2%5D%5E3+=+152+
(2) +s%5B2%5D%5E3%2A%28+1+-+8%2F27+%29+=+152+
(2) +s%5B2%5D%5E3%2A%28+19%2F27+%29+=+152+
(2) +s%5B2%5D%5E3+=+%2827%2F19%29%2A152+
(2) +s%5B2%5D%5E3+=+216+
(2) +s%5B2%5D+=+root%283%2C216%29+
(2) +s%5B2%5D+=+6+
and, since
(1) +s%5B1%5D+=+%282%2F3%29%2As%5B2%5D+
(1) +s%5B1%5D+=+%282%2F3%29%2A6+
(1) +s%5B1%5D+=+4+
The side of the bigger cube is 6
check:
+V%5B1%5D+=+4%5E3+
+V%5B2%5D+=+6%5E3+
and
(2) +V%5B2%5D+-+V%5B1%5D+=+152+
(2) +6%5E3+-+4%5E3+=+152+
(2) +216+-+64+=+152+
(2) +152+=+152+
OK