Question
A hemisphere is inscribed in a cube of side 6 cm. What is the volume of the hemisphere?
This question was previously asked in
SSC CGL 2025 Tier 1 Question Paper (25-Sep-2025) (Shift 3)
The correct answer is
56.55$cm^3$
A hemisphere inscribed in a cube of side 6 cm has the largest possible radius equal to half the side length of the cube, so \(r = \frac{6}{2} = 3\) cm.
The volume of a hemisphere is given by \(V = \frac{2}{3}\pi r^3\).
Substituting \(r = 3\): \(V = \frac{2}{3}\pi (3)^3 = \frac{2}{3}\pi \times 27 = 18\pi\).
Using \(\pi \approx 3.1416\): \(V = 18 \times 3.1416 \approx 56.55\) cm³.
Hence, the answer is 56.55 cm³.
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