Let the scale factor between the two similar figures be x.
Since the surface areas are proportional to the square of the scale factor, we have:
(567)/(1575) = x^2
x = sqrt((567/1575))
x = sqrt(0.36)
x = 0.6
Therefore, the volume of the smaller figure is proportional to the cube of the scale factor, so the volume of the smaller figure is:
V_smaller = (0.6)^3 * 2750
V_smaller = 0.216 * 2750
V_smaller = 594 incubed
Thus, the volume of the smaller figure is 594 cubic inches.
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. equals 567 insquared S.A. equals 1575 insquared V equals 2750 incubed
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