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From a cube of side 6 cm, a hemisphere of maximum volume is scooped out. What is the remaining volume?

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From a cube of side 6 cm, a hemisphere of maximum volume is scooped out. What is the remaining volume?
1. 216 - 12π
2. 216 - 18π
3. [27 - (2π/3) × 6]
4. 36 - (3π/3)
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Correct Answer - Option 2 : 216 - 18π

Side of cube a = 6 cm

⇒ Radius of hemisphere r = 6/2 = 3 cm

Volume of cube = a3 = 63 = 216 cm3

Volume of hemisphere = 2/3 × πr3 = 2/3 × π × 33 = 18π cm3

∴ Remaining volume = 216 – 18π cm3
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