A cylinder with a radius of 12 cm and height of 38 cm is cut parallel to the base into two pieces of different sizes. The total surface area of the larger piece formed is 60% of the total surface area of the given cylinder. The smaller piece is melted and used to create a sphere. Find the radius (in cm) of the sphere.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 6 × .
Radius of cylinder = 12 cm, height = 38 cm
Total surface area (TSA) = 2πr(h + r) = 2 × 3.14 × 12 × (38 + 12) = 1200π
Larger piece TSA = 60% of 1200π = 720π
TSA of larger piece = curved surface + 2 circular bases = 2πrh1 + 2πr² = 24π h1 + 288π
24π h1 + 288π = 720π → 24 h1 + 288 = 720 → 24 h1 = 432 → h1 = 18 cm
Smaller piece height = 38 - 18 = 20 cm
Volume of smaller piece = πr²h = π × 12² × 20 = 2880π
Volume of sphere = volume of smaller piece = (4/3) π R³
(4/3) π R³ = 2880π → R³ = 2880 × 3/4 = 2160
R = cube root of 2160 ≈ 6 × cm