Answer:
Since the figures are similar, their corresponding side lengths are proportional.
Let x be the scale factor between the larger and smaller figures. Then, the volume of the larger figure is x^3 times the volume of the smaller figure.
We can set up an equation to solve for x:
2500 = x^3 * 160
Divide both sides by 160:
x^3 = 2500/160
x^3 = 15.625
Take the cube root of both sides:
x = 2.5
So, the scale factor between the larger and smaller figures is 2.5.
Since surface area is proportional to the square of the scale factor, we can set up another equation to solve for the surface area of the smaller figure:
S.A. of smaller figure / S.A. of larger figure = (scale factor of smaller figure)^2 / (scale factor of larger figure)^2
Solving for the surface area of the smaller figure:
S.A. of smaller figure / 1400 = 2.5^2 / 1^2
S.A. of smaller figure / 1400 = 6.25
S.A. of smaller figure = 6.25 * 1400
S.A. of smaller figure = 8750
Therefore, the surface area of the smaller figure is 8750 meters squared.
Explanation: