Question
The volumes of two similar figures are given. The surface area of the larger figure is given. Find the surface area of the smaller figure.
Upper Vequals200 m cubed
Upper Vequals3125 m cubed
S.A.equals1575 m squared
Upper Vequals200 m cubed
Upper Vequals3125 m cubed
S.A.equals1575 m squared
Answers
GPT 3.5
Since the volumes of the two figures are in the ratio 200:3125, which simplifies to 8:125, the ratio of their surface areas will be the square of the ratio of their volumes. Therefore, the ratio of their surface areas is 64:15625.
Since the surface area of the larger figure is 1575 m^2, we can set up a proportion to find the surface area of the smaller figure:
1575 / 15625 = x / 64
Cross multiplying, we get:
15625x = 1575 * 64
15625x = 100800
x = 100800 / 15625
x ≈ 6.45
Therefore, the surface area of the smaller figure is approximately 6.45 m^2.
Since the surface area of the larger figure is 1575 m^2, we can set up a proportion to find the surface area of the smaller figure:
1575 / 15625 = x / 64
Cross multiplying, we get:
15625x = 1575 * 64
15625x = 100800
x = 100800 / 15625
x ≈ 6.45
Therefore, the surface area of the smaller figure is approximately 6.45 m^2.