The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:

#### Options

3

5

4

6

#### Solution

Let *r* and *h* be the radius and the height of the cylinder, respectively.

Given:

Diameter of the cylinder = 4 cm

∴ Radius of the cylinder, *r* = 2 cm

Height of the cylinder, *h* = 45 cm

Volume of the solid cylinder = `pir^2h=pixx(2)^2xx45 cm^2=180pi cm^3`

Suppose the radius of each sphere be *R* cm.

Diameter of the sphere = 6 cm

∴ Radius of the sphere, *R* = 3 cm

Let *n *be the number of solids formed by melting the solid metallic cylinder.

∴ *n* × Volume of the solid spheres = Volume of the solid cylinder

`=>nxx4/3 pi R^3=180pi`

`=>nxx4/3 pi(3)^3=180pi`

`=>n=(180xx3)/(4xx27)=5`

Thus, the number of solid spheres that can be formed is 5.

Hence, the correct option is B.