Question

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

Answer 1

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.