The number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 90cm and diameter 4 cm is:
Answer & explanation
Correct answer: option 1
Diameter of each sphere = 6 cm
then the radius = 3 cm
The height of cylinder = 90 cm
Diameter of the base of the cylinder = 4 cm
then the radius = 2 cm
Let the number of cylinders = n
So, according to the question,
n × πR2H = \(\frac{4}{3}\) πR3
= n × R2H = R3 \(\frac{4}{3}\)
= n × (2)2 × 90 = \(\frac{4}{3}\) × 33
= n = 10