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Question 54093This question is from textbook
: Explain how the ratio of volumes is related to the ratio of their sides. The figures are cubes. One cube's volume is 64 cubed cm (4*4*4) and the other cube's volume is 512 (8*8*8) So the ratio of their volumes would be 64:512, and the ratio of sides would be 6:6 since they're both cubes, but how is the ratio of volumes related to the ratios of their sides?? Thanks
This question is from textbook
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Explain how the ratio of volumes is related to the ratio of their sides. The figures are cubes. One cube's volume is 64 cubed cm (4*4*4) and the other cube's volume is 512 (8*8*8) So the ratio of their volumes would be 64:512, and the ratio of sides would be 6:6 since they're both cubes, but how is the ratio of volumes related to the ratios of their sides?? Thanks
in general for similar figures as is your case
if side is increased by .....x times..say 2 times
area = side * side = x*x=x^2....hence area increases by x^2 times...say 2^2= 4times
volume = side*side*side =x*x*x=x^3...hence volume increase by x^3 times =2^3=8 times as you got.
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