The volume of the cube is 180. Find the volume of a triangular prism cut off from it by a plane passing through the midpoints
| May 9, 2021 | education
The volume of the cube is 180. Find the volume of a triangular prism cut off from it by a plane passing through the midpoints of two edges going out of one vertex and parallel to the third edge going out of this vertex.
A plane parallel to an edge will pass through the midpoints of a pair of edges adjacent to it at both ends. It will cut a triangular prism from the cube. The base area of the prism will be 8 times smaller than the cube face. Consequently, the volume of the prism will relate to the volume of the cube as the area of the base of the prism to the area of the face of the cube.
Vp / Vk = 1/8;
Vp = Vk / 8 = 180/8 = 22.5.
Answer: 22.5.
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