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 = 522 in^2
S.A = 1450 in^2
V = 2750 in^3
Please help asap!!
Since the figures are similar, their corresponding sides are proportional to each other. Let's call the ratio of the corresponding sides x:y, where x is the length of the side of the smaller figure and y is the length of the side of the larger figure.
The ratio of their surface areas is the square of the ratio of their corresponding sides:
(x/y)^2 = 522/1450
Solving for x/y, we get:
x/y = sqrt(522/1450) ≈ 0.573
So, the volume of the smaller figure is proportional to the cube of this ratio:
V_small/V_large = (x/y)^3
V_small/2750 = (0.573)^3
V_small ≈ 632.7 in^3
Therefore, the volume of the smaller figure is approximately 632.7 in^3.