A cylinder of radius 10 cm and height 30 cm is cut, parallel to the base, into two pieces of different sizes. The total surface area of the larger piece formed is 70% of that of the given cylinder. The smaller piece is melted and made into a sphere. The radius (in cm) of the sphere is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e .
The total surface area (TSA) of the original cylinder = 2πr(r + H)
TSA = 2π(10)(10 + 30) = 2π(10)(40) = 800π cm²
The total surface area of the larger piece = 0.70 × TSAoriginal
TSAlarge = 0.70 × 800π
TSAlarge = 560π cm²
so,
TSAlarge = 2πrh1 + 2πr2
560π = 2π(10)h1 + 2π(10)2 = 20πh1 + 200π
360π = 20πh1
h1 = 360/20 = 18 cm
Volume of the Smaller Piece = h2 = 30 − 18 = 12 cm
The smaller piece is a cylinder with a radius of 10 cm and a height of 12 cm.
Volumesmall = πr2h2
Volumesmall = π(10)2(12)
Volumesmall = 1200π cm³
Radius of the Sphere
Volumesphere = Volumesmall
(4/3)πR3 = 1200π
R3 = 1200×(3/4) = 300 × 3 = 900 ⇒ R =