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:

10

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