Subjects geometry

Third Prism

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Third Prism


1. The problem states that two bricks can be placed face-to-face to form three different rectangular prisms, and two of these prisms are shown. We need to find the measurements of the third prism. 2. Let's analyze the given options and the dimensions of the bricks. Since the prisms are formed by placing two bricks face-to-face, the dimensions of the prisms are combinations of the bricks' dimensions. 3. The first prism has dimensions $11 \text{ cm} \times 16 \text{ cm} \times 10 \text{ cm}$. 4. The second prism has dimensions $22 \text{ cm} \times 20 \text{ cm} \times 8 \text{ cm}$. 5. Notice that the second prism's dimensions are roughly double or related to the first prism's dimensions, indicating the bricks are combined differently. 6. To find the third prism, we look for a combination of dimensions that uses the bricks' dimensions but is different from the first two prisms. 7. Checking the options: - A: $11 \times 16 \times 10$ (already the first prism) - B: $22 \times 20 \times 8$ - C: $32 \times 22 \times 10$ - D: $44 \times 16 \times 5$ 8. Since the first two prisms are A and B, the third prism must be either C or D. 9. The third prism should be formed by combining the bricks in a way that the dimensions add up accordingly. Option C ($32 \times 22 \times 10$) fits as a plausible combination of the bricks' dimensions. 10. Therefore, the measurements of the third prism are $32 \text{ cm} \times 22 \text{ cm} \times 10 \text{ cm}$. **Final answer:** Option C: $32 \text{ cm} \times 22 \text{ cm} \times 10 \text{ cm}$.