SSC CGL 2025 PYQ — Question 65

The correct answer is option 1 i.e. 47.67%.

Let cube side = a

Cube volume = a³

Sphere radius = a/2

Sphere volume = (4/3)π(a/2)³ = (π/6)a³

Unoccupied volume = a³ – (π/6)a³ = a³(1 – π/6)

Percentage unoccupied $=\frac{a^3(1 – \frac{\pi}{6}) }{a^3}\times100$

= (1 – π/6) × 100

= (1 - 3.1416/6) × 100

= (1 - 0.5236) × 100

= 0.4764 × 100

≈ 47.67%