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.

The radius of a metal sphere at room temperature T is R, and the coeff

1.	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.
Answer» `2pi" "Ralpha" "DeltaT` `piR^(2)" "alpha" "DeltaT` `4/3pi" "R^(3)" "alpha" "DeltaT` `4pi" "R^(3)" "alpha" "DeltaT` Solution :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`