A sphere-shaped casting solidifies on 10 min. What will be the solidification time in minutes for another sphere of the same material, which is 8 times heavier than the original casting ?

Concept:

Solidification time(τ):

Solidification time for molten metal in mold is given by 

τ = k₁M² , k₁ = mold constant or solidification factor, M = Modulus 

M= 

For sphere, M = 

Calculation:

Given:

τ₁ = 10 min, V₂ = 8V₁, τ₂ =?

Now, we know that

 V2 = 8V1 ⇒ (D₂)³ = 8 (D₁)³⇒ D₂= 2D₁

From the above equation,

∴ τ₂ = 40 min