To find the volume of solid B, you can use the concept of similarity. Since the solids are similar, their volumes are proportional to the cubes of their corresponding dimensions (in this case, height).
1. The ratio of the height of solid A to the height of solid B is 2:5. This means that the height of solid A is 2 units and the height of solid B is 5 units.
2. Given that the volume of solid A is 12 cm³, we can calculate the volume of solid B using the ratio of their heights.
3. Since the volumes of similar solids are proportional to the cubes of their dimensions, the volume ratio will be the cube of the height ratio. In this case, (2/5)³ = 8/125.
4. Now, if the volume of solid A is 12 cm³, you can find the volume of solid B by setting up a proportion: 12/1 = x/8/125. Cross multiply to solve for x, which represents the volume of solid B.
5. Calculate x to find the volume of solid B in cubic centimeters. This process will help you determine the volume of solid B based on the given information about the solids' similarity and the volume of solid A.