Find the ratio for the similar figure.
If the area ratio is 4:49,
what is the volume ratio?
(√4:√49)^3 = (2:7)^3 = 8:343
To find the volume ratio of similar figures when given the area ratio, we need to know the relationship between the areas and volumes of these figures.
In general, when two similar figures or objects are scaled up or down proportionally, the ratio of their areas is equal to the square of the scale factor, and the ratio of their volumes is equal to the cube of the scale factor.
In this case, the area ratio is given as 4:49. Since the scale factor for the areas is the square root of the ratio, we can find it by evaluating:
sqrt(4/49) = 2/7
So, the scale factor for the areas is 2/7.
Now, to find the volume ratio, we need to cube this scale factor:
(2/7)^3 = 8/343
Therefore, the volume ratio for the similar figure is 8:343.