Maths Olympiad Prep

Track / Stage 4 / 141 of 340 #401 of 1964

Problem 401

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

7.3. 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.

Official solution

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

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.