The minute hand of a clock is 12 cm long.

Angle described by the minute hand in 60 minutes $=360^{\circ}$

Angle described by the minute hand in 35 minutes $=\left(\frac{360}{60} \times 35\right)^{\circ}$

$=210^{\circ}$

Now,

$r=12 \mathrm{~cm}$ and $\theta=210^{\circ}$

$\therefore$ Required area swept by the minute hand in 35 minutes = Area of the sector with $r=12 \mathrm{~cm}$ and $\theta=210^{\circ}$

$=\frac{\pi r^{2} \theta}{360}$

$=\left(\frac{22}{7} \times 12 \times 12 \times \frac{210}{360}\right) \mathrm{cm}^{2}$

$=264 \mathrm{~cm}^{2}$