Question
A perfect cube with a side length of 8 cm has the largest possible sphere fitted inside it. What is the volume of the empty space within the cube?
This question was previously asked in
SSC CGL 2025 Tier 1 Question Paper (25-Sep-2025) (Shift 3)
The correct answer is
512 - 256π/3 cm^3
The volume of the cube with side 8 cm is \(V_{cube} = 8^3 = 512\) cm³.
The largest sphere that fits inside the cube has a diameter equal to the cube's side, so its radius is \(r = \frac{8}{2} = 4\) cm.
The volume of this sphere is \(V_{sphere} = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (4)^3 = \frac{4}{3}\pi \times 64 = \frac{256\pi}{3}\) cm³.
The empty space is \(V_{cube} - V_{sphere} = 512 - \frac{256\pi}{3}\) cm³.
Hence, the answer is 512 - 256π/3 cm³.
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