Question

Prove that alpha: beta:gamma= 1:2:3

Answer 1

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$\boxed{\boxed{\bold{\alpha : \beta : \gamma = 1:2:3}}}$

♣  Alpha (α) is coefficient of linear expansion.
♦  Increase in length during expansion is called linear expansion.
It means object one side increases.
Hence α = 1

♣ Beta (β) is coefficient of superficial expansion.
♦ Increase in area during expansion is called superficial expansion.
We know area = Length × Breadth
No. of sides = 2
Hence, β = 2

♣ Gamma ($\gamma$) is coefficient of cubical expansion.
♦ Increase in volume during expansion is called cubical expansion.
We know, volume = Length × Breadth × Height
No. of sides = 3
Hence, $\gamma$ = 3

So, $\boxed{\boxed{\bold{\alpha : \beta : \gamma = 1:2:3}}}$

Hence Proved!

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