Question

. The number of solid spheres, each of diameter
6 c.m. that could be moulded to form a solid
cylinder of height 45 c.m. and diameter 4 c.m.
​

Answer 1

Diameter of the sphere = 6 cm

So, Radius = 6/2 = 3 cm

Height of the solid cylinder = 45 cm

Diameter of the solid cylinder = 4 cm

So, Radius of the sphere = 4/2 = 2 cm

Volume of the sphere = 4/3 πr³

= 4/3 π × 2³

= 4/3 π × 8

= 32π/3

Volume of the solid cylinder = πr²h

= π × 3² × 45

= π × 9 × 45

= 405π

Let the number of spheres be x

According to the question :

32π/3 ×. x = 405π

x = (405π × 3)/32π

x = (405 × 3)/32

x = 1215/32

x = 37.96875

x = 38 (approx)

38 spheres are the number of spheres from which cylinder is moluded.