The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is `alpha`. The sphere is heated a little by a temperature `DeltaT` so that its new temperature is `T+DeltaT`. The increase in the volume of the sphere is approsimately.

Options

A. `2pi" "Ralpha" "DeltaT`
B. `piR^(2)" "alpha" "DeltaT`
C. `4/3pi" "R^(3)" "alpha" "DeltaT`
D. `4pi" "R^(3)" "alpha" "DeltaT`

Answer

D

Explanation

Suppose, radius of sphere is R in room temperature T. Radius increases with increase in T.

Original volume of sphere `V_(0)=4/3piR^(3)`
Coefficient of linear expansion = `alpha`
Coefficient of volume expansion `=3alpha`
`:.(DeltaV)/(V DeltaT)=3alpha`
`:.DeltaV=2alphaVDeltaT`
But `V=4/3piR^(3)`
`:.Delta=4piR^(3)alphaDeltaT`