Question

Find the number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metallic cylinder of height 45 cm and diameter 4 cm.

Answer 1

We have,

Radius of the sphere, R `= 6/2 = 3  "cm" `

Radius of the cylinder, `"r" = 4/2 = 2  "cm"` and

Height of the cylinder, h = 45 cm

Now, 

The number of solid spheres `= "Volume of the cylinder"/"Volume of the sphere"`

`=(pi"r"^2"h")/((4/3pi"R"^3))`

`=(3"r"^2"h")/(4"R"^3)`

`=(3xx2xx2xx45)/(4xx3xx3xx3)`

= 5

So, the number of solid spheres so moulded is 5.