The volumes of two similar solids are 1,728 m3 and 343 m3. The surface area of the larger solid is 576 m2. What is the surface area of the smaller solid?
(1 point)
Responses
196 m2
196 m 2
76 m2
76 m 2
1,372 m2
1,372 m 2
392 m2
To find the surface area of the smaller solid, we can use the concept of similarity. Since the volumes of the two solids are in a ratio of 1,728 m^3 to 343 m^3, the side lengths of the solids will be in a ratio of the cube root of 1,728 to the cube root of 343.
Taking the cube root of 1,728, we get 12.
Taking the cube root of 343, we get 7.
Therefore, the ratio of the side lengths of the two solids is 12:7.
Since the surface area is a function of the square of the side length, we can find the ratio of the surface areas by squaring the ratio of the side lengths.
(12/7)^2 = 144/49
Therefore, the ratio of the surface areas is 144:49.
Since the surface area of the larger solid is given as 576 m^2, we can set up the following proportion:
576 m^2 / 144 = x / 49
Solving for x, we get:
x = (576 m^2 * 49)/144 = 196 m^2
Thus, the surface area of the smaller solid is 196 m^2.
Therefore, the correct answer is 196 m2.