2022 AMC 8 Problem 24
Attempt Problem 24 of the 2022 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
The figure below shows a polygon consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that:
and
What is the volume of the prism?
Answer: C
Small hint:
Find the right-triangle base of the prism
Big hint:
The folded net gives a base with legs and , and prism length
Solution:
When the net is folded, the matching side lengths give . Since is a rectangle, . The fold identifies with , so . In rectangle , this gives , and the opposite side equals .
Since , we have . Thus one triangular base of the prism is right triangle , with area The prism length is , so the volume is .
Thus, the correct answer is C.
Problem 24 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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- 1993 AMC 8
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