Problem: a right circular cone is exactly fitted inside a cube in such away that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube . if the volume of the cube is 343 cc , what approximately is the volume of the cone ?
Rationale: edge of the cube = 3 √ 334 = 7 cm ∴ radius of cone = 3.5 cm height = 7 cm volume of cone = 1 ⁄ 3 π r 2 h 1 ⁄ 3 π r 2 h = 1 ⁄ 3 × 22 ⁄ 7 × ( 3.5 ) 2 × 7 = 1 ⁄ 3 × 22 × 12.25 ≈ 90 sec answer b
annotated_formula: volume_cone(divide(cube_edge_by_volume(343), const_2), cube_edge_by_volume(343))