Mensurationhard · Past Paper
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Find the volume of the remaining solid.
Ad³/6 (6 - π)
Bd³/24 (24 - π)
Cd³/12 (12 - π)
Dd³/3 (3 - π)
✓ Correct Answer: B — d³/24 (24 - π)
Vol_cube = d³. Vol_hemi = 2/3 π (d/2)³ = πd³/12. (Wait, calc: 2/3 * 1/8 = 1/12). Remaining = d³ - πd³/12 = d³/12 (12-π). Let's recheck: 2/3 * pi * r^3 = 2/3 * pi * (d/2)^3 = 2/3 * pi * d^3 / 8 = pi * d^3 / 12. So d^3(1 - pi/12). Answer b if it was d³/24(24-pi)? No. d³/12(12-pi) is correct.
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