Question

The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.

Upper Vequals3125 m cubed
Upper Vequals200 m cubed
S.A.equals260 m squared
Question content area bottom
Part 1
The surface area of the larger figure is
  
enter your response here m squared.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The surface area of the larger figure is 1040 m squared.

To find the surface area of the larger figure, we need to use the ratio of the volumes to find the ratio of the side lengths, and then use this ratio to find the surface area.

First, find the ratio of the volumes:
V(larger figure) / V(smaller figure) = 3125 / 200 = 15.625

Next, find the ratio of the side lengths (since the volumes are cubed, the ratio will be cubed as well):
∛15.625 ≈ 2.5

Now, use this ratio to find the surface area of the larger figure:
S.A.(larger figure) = (2.5)^2 * S.A.(smaller figure) = 6.25 * 260 = 1040 m squared

Therefore, the surface area of the larger figure is 1040 m squared.