The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.
S.A. = 216in^2
S.A. = 486in^2
V = 567in^3
Let the ratio of the surface areas be x:1, where x is the scale factor of the similar figures.
Solving for x:
216/x = 486/1
216 = 486x
x = 216/486
x = 2.25
Since volume is the cubic factor, the ratio of volumes will be x^3:
V_large/V_small = (2.25)^3
V_large/V_small = 11.39
Now, we know the volume of the larger figure V_large = 567in^3.
So, the volume of the smaller figure V_small can be found by:
567/V_small = 11.39
V_small = 567/11.39
V_small ≈ 49.74 in^3
Therefore, the volume of the smaller figure is approximately 49.74 in^3.