The radious of a metal sphere at room temperature T is R, and the coefficient of linar expansion of the metal is `alpha`. The sphere is heated a little by a temperature `Delta T` so that its new temperature is `T+ Delta T`. The increase in the volume of the sphere is approximately

Options

A. `2pi R alpha Delta T`
B. `pi R^(2) alpha Delta T`
C. `4 pi R^(3) alpha Delta t//3`
D. `4 pi R^(3) alpha Delta T`

Answer

D

Explanation

Let V be the volume of sphere of radiuas R at temp. T, then `V=(4)/(3) pi R^(3)`.
Increase in volume of sphere with rise in temperature `Delta T` is
`Delta V= gamma V Delta T =3alphaxx(4)/(3) pi R^(3) Delta T =4pi R^(3) alpha Delta T`