The surface tension of soap solution is 3 . 5 × 10 ^ - 2 N m ^ - 1...

The amount of work done is equal to the change in the surface energy to increase the radius of the bubble.

The formula to calculate the change in surface energy is given by

$\DeltaU = 2 ( T \times \DeltaA ) . . . \left(1\right)$

Substitute the values of the known parameters into equation (1) to calculate the required work done.

$\begin{cases}∆ U & = & 3 . 5 \times {10}^{- 2} \times 4\pi\left[( 0 . 2{)}^{2} - ( 0 . 1{)}^{2}\right] \times 2J \\ = & 3 . 5 \times {10}^{- 2} \times 4 \times \dfrac{22}{7} \times 0 . 03 \times 2 \\ = & 2 \times 1 . 32 \times {10}^{- 2} \\ = & 264 \times {10}^{- 4}J\end{cases}$