An aluminium sphere of `20cm` diameter is heated from `0^(@)C` to `100^(@)C`. Its volume changes by (given that the coefficient of linear expanison for aluminium `(alpha_(Al) = 23 xx 10^(-6//0)C)`

Options

A. 2.89 cc
B. 9.28 cc
C. 49.8 cc
D. 28.9 cc

Answer

D

Explanation

`V = V_0 (1+ gamma Delta T)`
As we know the relation , `gamma = 3 alpha`
` Delta V = V_0 (3 alpha) Delta T`
`Delta V = 4/3 xx 3.141 xx (10 cm)^3 xx (3 xx 23 xx 10^(-6) ) xx (100 - 0)`
` Delta V = 28.9 ` cc