Question

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!!

Answer 1

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.