2019 · Q93
Consider the following for the next three (03) items:
A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular cone is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.
What is the ratio of the volume of the sphere to that of the cone?
Elementary MathematicsMensuration
- A6√3:1
- B7:2
- C3√3:1
- D5√3:1
Explanation
Sphere volume = (4/3)π(s√3/2)^3 = π√3s^3/2. Cone volume = (1/3)π(s/2)^2·s = πs^3/12. Ratio = (π√3s^3/2)/(πs^3/12) = 6√3 : 1.