Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is ' α prime. The metal sheet is heated uniformly, by a small temperature Δ T , so that its new temperature is T +Δ T. Calculate the increase in the volume of the metal box.

Question

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is ' α prime. The metal sheet is heated uniformly, by a small temperature Δ T , so that its new temperature is T +Δ T. Calculate the increase in the volume of the metal box. (A) 3 a 3 α Δ T (B) 4 a 3 α Δ T (C) 4 π a 3 α Δ T (D) (4/3) π a 3 α Δ T

Tardigrade Admin · Accepted Answer

Δ V = V &gamma; Δ T Δ V =3 a 3 α Δ T

$3 a^{3} α Δ T$

$4 a^{3} α Δ T$

$4 π a^{3} α Δ T$

$\frac{4}{3} π a^{3} α Δ T$

$Δ V = Vγ Δ T$
$Δ V = 3 a^{3} α Δ T$

3a3αΔT

4a3αΔT

4πa3αΔT

34​πa3αΔT

ΔV=VγΔT ΔV=3a3αΔT

$3 a^{3} α Δ T$

$4 a^{3} α Δ T$

$4 π a^{3} α Δ T$

$\frac{4}{3} π a^{3} α Δ T$

$Δ V = Vγ Δ T$
$Δ V = 3 a^{3} α Δ T$