A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted to form a solid cylinder of base diameter 8 cm. What is the height of the cylinder?
Answer & explanation
Correct answer: option 3
Volume of hollow sphere = \(\frac{4 }{3 }\)π(R3 -r3)
Volume of solid cylinder = πR2h
According to the question,
\(\frac{4 }{3 }\)π(R3 -r3) = πR2h
\(\frac{4 }{3 }\) x (43 - 23) = 42h ( π gets cancelled)
\(\frac{4 }{3 }\) x 64 - 8 = 16h
\(\frac{4 }{3 }\) x 56 = 16h
h = \(\frac{224 }{48 }\)
h = 4.67 cm