A solid metal ball of radius 12 cm is melted and made into 27 equal small balls…

Step 1. The radius. $27 \times \dfrac{4}{3}\pi r^3 = \dfrac{4}{3}\pi \times 12^3$ gives $r^3 = \dfrac{1728}{27} = 64$, so $r = 4\ \text{cm}$.

Step 2. The big ball's area. $4\pi \times 144\ \text{cm}^2 = 576\pi\ \text{cm}^2$.

Step 3. The small balls' area. $27 \times 4\pi \times 16\ \text{cm}^2 = 1728\pi\ \text{cm}^2$.

Step 4. The ratio. $\dfrac{1728\pi}{576\pi} = 3$, which is $\sqrt[3]{27}$. The area has become three times as large.

Step 5. The increase. $(3 - 1) \times 100 = 200$ percent.