SOLUTION: The surface areas of two cubes are in the ratio of 49:81. If the volume of the smaller cube is 20, what is the volume of the larger cube?

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Question 149521: The surface areas of two cubes are in the ratio of 49:81. If the volume of the smaller cube is 20, what is the volume of the larger cube?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the ratio of the surface areas is 49:81, this means that

ratio_surface_area=49%2F81


Now simply take the square root of the fraction to get the ratio of the sides.

sqrt%2849%2F81%29=sqrt%2849%29%2Fsqrt%2881%29=7%2F9

So the ratio of the sides is 7:9


Now simply cube 7%2F9 to get the ratio of the two volumes

7%5E3%2F9%5E3=343%2F729

Now let x=volume of the larger cube

Since the ratio of the two volumes, this means that we can say

20%2Fx=343%2F729


20=%28343%2F729%29%2Ax Multiply both sides by x


20%2A729=343%2Ax Multiply both sides by 729


14580=343%2Ax Multiply


14580%2F343=x Divide both sides by 343



So our answer is x=14580%2F343 which is approximately x=42.51


So the volume of the larger cube is 42.51