How many metallic spheres, each of diameter 6 cm can be melted to mould into a solid cylinder of diameter 8 cm and height of 18 cm?

8

We know that,

V₁ = \(\frac{4}{3}\) πr₁³

V₂ = πr²h

 r₁ = radius of the sphere, r₂ = radius of the cylinder 

V₁ = Volume of Sphere, V₂ = Volume of Cylinder

H = height

We have,

Diameter of the sphere = 6cm

Diameter of the cylinder = 8cm

Height = 18cm

Then according to the question,

Let the number of metallic spheres  = a 

r₁ = 3 cm , r₂ = 4 cm , h = 18 cm 

= a × \(\frac{4}{3}\) πr₁³ = πr₂² × h 

= a × \(\frac{4}{3}\) × 3³ = 4² × 18 

= a = 8