The volumes of two similar solids are 729 m and 125 m. The surface area of the larger solid is 324 m. What is the surface area of the smaller solid? a56 m b100 m c500 m d200 m

The ratio of the volumes of two similar solids is the cube of the ratio of their corresponding lengths. Similarly, the ratio of their surface areas is the square of the ratio of their corresponding lengths.

1. First, find the ratio of the volumes. This is 729/125 = 5.832.

2. The cube root of this ratio gives the ratio of the corresponding lengths. The cube root of 5.832 is approximately 1.8.

3. The square of this ratio gives the ratio of the surface areas. The square of 1.8 is approximately 3.24.

4. To find the surface area of the smaller solid, divide the surface area of the larger solid by this ratio. This is 324/3.24 = 100 m.

So, the surface area of the smaller solid is 100 m². The answer is (b) 100 m.

The ratio of the volumes of two similar solids is the cube of the ratio of their corresponding lengths. So, the ratio of their volumes is cube root of (729/125) = 3/5.

The ratio of their surface areas is the square of the ratio of their corresponding lengths. So, the ratio of their surface areas is (3/5)^2 = 9/25.

Therefore, the surface area of the smaller solid is (9/25) * 324 = 116.64 m.

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