Find 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.

Given, diameter of sphere = 6 cm

We know that radius is half of the diameter.

∴ Radius of sphere, r₁ = 3 cm

Given, height of solid metal cylinder, h = 45 cm

Diameter = 4 cm

∴ Radius of cylinder, r₂ = 2 cm

Let a cylinder be melted to form n number of spheres.

So, Volume of cylinder = Volume of n spheres

We know that volume of cylinder = πr²h

And volume of sphere = (4πr³)/3

∴ π (4)(45) = (n ×(4π(3)³)/3

180π = n36π

⇒ n = 180/36

⇒ n = 5

Ans. 5 spheres can be made by melting the cylinder.