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.
V = 8ft^3
V = 125ft^3
S.A. = 4ft^2
S.A. = 62.5
To find the surface area of the larger figure, we can use the concept of similarity between the figures. Similar figures have the same shape but may differ in size.
The volumes of two similar figures are given as V1 = 8ft^3 for the smaller figure and V2 = 125ft^3 for the larger figure. The relationship between volumes of similar figures is given by the cube of the scale factor.
Therefore, the ratio of the volumes of the two figures is (V2/V1)^(1/3), which gives us a scale factor of V2^(1/3) / V1^(1/3).
In this case, the scale factor is (125ft^3)^(1/3) / (8ft^3)^(1/3) = 5ft / 2ft = 5/2.
Since the surface area of a figure is proportional to the square of the scale factor, we can find the ratio of the surface areas as (5/2)^2 = 25/4.
Given that the surface area of the smaller figure is S.A. = 4ft^2, we can find the surface area of the larger figure by multiplying it by this ratio:
Surface area of the larger figure = (S.A. of the smaller figure) * (ratio of surface areas)
Surface area of the larger figure = 4ft^2 * (25/4)
Surface area of the larger figure = 25ft^2
Thus, the surface area of the larger figure is 25ft^2.