A non-isotropic solid metal cube has coefficients of linear expansion as: 5×10−5/0C along the x-axis and 5×10−6/0C along the y and the z-axis. If the coefficient of volume expansion of the solid is C×10−6/0C then the value of C is________.

Volume, V=Ibh⇒ ΔVV=Δll+Δbb+Δhh∴ γ=ΔVVΔT=ΔllΔT+ΔbbΔT+ΔhhΔT⇒ γ=5×10−5+5×10−6+5×10−6=60×10−6/0C∴ Value of C=60.00

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A non-isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10^{- 5} /^{0} C$ along the x-axis and $5 \times 10^{- 6} /^{0} C$ along the $y$ and the z-axis. If the coefficient of volume expansion of the solid is $C \times 10^{- 6} /^{0} C$ then the value of $C$ is________.

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answer is 60.

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Volume, $V = I b h \Rightarrow \frac{Δ V}{V} = \frac{Δ l}{l} + \frac{Δ b}{b} + \frac{Δ h}{h}$

$∴ γ = \frac{Δ V}{V Δ T} = \frac{Δ l}{l Δ T} + \frac{Δ b}{b Δ T} + \frac{Δ h}{h Δ T}$

$\Rightarrow γ = 5 \times 10^{- 5} + 5 \times 10^{- 6} + 5 \times 10^{- 6} = 60 \times 10^{- 6} /^{0} C$

$∴$ Value of $C = 60.00$

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