Question

The ratio of the surface area of two cubes is 49:81 . Find the ratio of their volume.​

Answer 1

Answer:

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

Answer 2

Answer:

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