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?

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) (Show Source): You can put this solution on YOUR website!
Since the ratio of the surface areas is 49:81, this means that

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

So the ratio of the sides is 7:9

Now simply cube to get the ratio of the two volumes

Now let x=volume of the larger cube

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

Multiply both sides by x

Multiply both sides by 729

Multiply

Divide both sides by 343

So our answer is which is approximately

So the volume of the larger cube is 42.51
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