Multiple choice

A right circular solid cone of radius 3.2 cm and height 14.4 cm is melted and recast into a right circular cylinder of height 19.2 cm. What is the diameter of the base of the cylinder ?

  1. 3.2 cm

  2. 4.5 cm

  3. 3.5 cm

  4. 4.2 cm
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A Correct answer
Explanation

Volume of cone = (1/3)πr²h = (1/3)π(3.2)²(14.4) = (1/3)π × 10.24 × 14.4 = 49.152π. Volume of cylinder = πR²H = πR²(19.2). Equating: πR²(19.2) = 49.152π. R² = 49.152/19.2 = 2.56. R = 1.6. Diameter = 2R = 3.2 cm.

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