Multiple choice

A solid hemisphere has radius 42 cm. It is melted to form a cylinder such that its curved surface area and the total surface area are in ratio 3: 4. Find the radius of the cylinder.

  1. 12.7 cm

  2. 25.44 cm

  3. 36.10 cm

  4. 49.36 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume conservation: (2/3)π(42)³ = πr²h. Hemisphere volume = 49,392π cm³. For the cylinder, curved surface area = 2πrh and total surface area = 2πr(r+h). Given 2πrh/[2πr(r+h)] = 3/4, we get h/r = 2. Solving with volume gives r = 25.44 cm.

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