2022 · Q63
The surface area of a cube of length x is equal to the surface area of a sphere of radius y. Consider the following statements :
- 12x > 3y2. The volume of the cube is greater than the volume of the sphere.
Which of the above statements is/are correct?
Elementary MathematicsMensuration
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
6x² = 4πy²; then 2x > 3y would need π > 27/8 = 3.375, false. Also the cube's volume (2π/3)^{3/2}y³ ≈ 3.03y³ is less than the sphere's (4/3)πy³ ≈ 4.19y³, so statement 2 is false. Hence the keyed option is D.