A right circular cone is inscribed in a cube such that its base coincides with the base of the cube and vertex lies on the top face center. What fraction of the cube's volume does the cone occupy?
Show answer & explanation
Correct answer: C
Explanation
Side of the cube = a, Base of the cone = Base of the cube, Height = a
According to the formula:
Volume of the cone = (1/3)πr²h
Volume of the cube = a³
⇒ r = a/2
Volume of the cone = (1/3)π(a/2)² × a = (1/12)πa³
Ratio = (1/12)πa³ / a³ = π/12