SOLUTION: A bottling company manufactures a bottle that has a volume of 243 milliliters. The company wants to make a new bottle that has dimensions 3 times smaller than the original. What wi

Algebra ->  Volume -> SOLUTION: A bottling company manufactures a bottle that has a volume of 243 milliliters. The company wants to make a new bottle that has dimensions 3 times smaller than the original. What wi      Log On


   



Question 1023033: A bottling company manufactures a bottle that has a volume of 243 milliliters. The company wants to make a new bottle that has dimensions 3 times smaller than the original. What will be the new volume of the new bottle?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
To make it simple, I'll say the bottle is a cube
with volume +243+ ml3
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Each side of this cube is:
+s%5E3+=+243+
+s+=+6.24025+
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Make the side 3 times smaller
+s%2F3+=+2.080084+
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Find the volume of the new cube
with this side length
+V+=+2.080084%5E3+
+V+=+9+ ml3 is the new volume
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Another way to arrive at this is:
+s%5E3+=+243+
+%28+s%2F3+%29%5E3+=+s%5E3%2F27+
This is the new volume with +s%2F3+ side length
Since +s%5E3+=+243+, I can say:
+%28+s%2F3+%29%5E3+=+243%2F27+
+%28s%2F3+%29%5E3+=9+
The new volume is +9+ ml3