A small liquid drop of radius R is divided into 27 identical liquid...

Let radius of the newly formed drops be $r$.

As total volume will remain constant, therefore

$\dfrac{4}{3}\pi{R}^{3} = 27 \times \left(\dfrac{4}{3} \times \pi{r}^{3}\right)$

$⇒ {R}^{3} = 27{r}^{3}$

$⇒ R = 3r$

$⇒ r = \dfrac{R}{3}$

$⇒ {r}^{2} = \dfrac{{R}^{2}}{9}$

Now, work done $= T \times \DeltaA$

$= T\left[27\left(4\pi{r}^{2}\right)\right] - T\left[4\pi{R}^{2}\right] = T\left[27\left(4\pi\dfrac{{R}^{2}}{9}\right)\right] - T\left[4\pi{R}^{2}\right] = T\pi{R}^{2}\left(12 - 4\right)$

$= 8\pi{R}^{2}T$