2019 · Q91
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.
Consider the following statements:
- 1The surface area of the sphere is √5 times the curved surface area of the cone.
- 2The surface area of the cube is equal to the curved surface area of the cylinder.
Which of the above statements is/are correct?
Elementary MathematicsMensuration
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Let the cube have side s. Sphere radius = s√3/2, so sphere SA = 4π(3s^2/4) = 3πs^2. Cone: radius s/2, height s, slant l = s√5/2, CSA = π(s/2)(s√5/2) = πs^2√5/4; ratio 3πs^2/(πs^2√5/4) = 12/√5 ≠ √5, so statement 1 is false. Cube SA = 6s^2 vs cylinder CSA = πs^2: statement 2 is false. Neither is correct.