Maths Olympiad Prep

Track / Stage 4 / 165 of 340 #425 of 1964

Problem 425

AMC 12 late, AIME early
Geometry Difficulty 4.7 Find the answer

Find the volume of a regular triangular pyramid, the midpoint of the height of which is at a distance of 2 and 10\sqrt{10} from the lateral face and the lateral edge, respectively. Round your answer to two decimal places if necessary.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Answer: 309.84 (exact value: 801580 \sqrt{15} ).

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.