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'. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temeprature is T + ΔT. Calculate the increase in the volume of the metal box.

Options

• `4/3pialpha^3Delta"T"`

• 4πa³ αΔT

• 3a³ αΔT

• 4a³ αΔT

Answer 1

3a³ αΔT

Explanation:

Length of metal sheet of cube = a

Room temperature =T

Coefficient of liner expansion of metal sheet = α

Increase in temperature = ΔT 

New temperature = T + ΔT

Now, ΔV = V ·ϒ· ΔT

⇒ ΔV = a³·ϒ· ΔT

⇒ ΔV = a³ (3α). ΔT       ..(∵ ϒ = 3α)

⇒ ΔV = 3a³ αΔT