Multiple choice

A hemisphere of iron is melted and recast in the shape of a right circular cylinder of diameter 18 cm and height 162 cm. The radius of the hemisphere is

  1. 27 cm

  2. 9 cm

  3. 6 cm

  4. 12 cm
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A Correct answer
Explanation

When a solid is melted and recast, its volume remains constant. Volume of hemisphere = (2/3)πr³. Volume of cylinder = πR²h, where R = 9 cm (diameter/2) and h = 162 cm. Equating: (2/3)πr³ = π(9)²(162) = π(81)(162). Simplifying: (2/3)r³ = 81 × 162 = 13122. So r³ = 13122 × 3/2 = 19683. Since 27³ = 19683, the radius of hemisphere is 27 cm.

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