The temperature of a metallic sphere of radius R is increased by a small amount T . If the linear coefficient of thermal expansion of the metal is , the approximate increase in the volume of the sphere is :

Step-by-step solution

The initial volume of the metallic sphere is V = 4 3 R^3 . The coefficient of volume expansion is related to the linear coefficient of thermal expansion as = 3 . The increase in volume V due to a temperature increase T is given by V = V T . Substituting the values of V and , we get: V = ( 4 3 R^3 )(3 ) T V = 4 R^3 T Answer: 4 R^3 T