In a circle of radius 10 cm,

We have given the radius of the circle and angle subtended at the centre of the circle.

$r=10 \mathrm{~cm}$

$\theta=108^{\circ}$

Now we will find the area of the sector.

Area of the sector $=\frac{\theta}{360} \times \pi r^{2}$

Substituting the values we get,

Area of the sector $=\frac{108}{360} \times \pi \times 10^{2}$....(1)

Now we will simplify the equation (1) as below,

Area of the sector $=\frac{3}{10} \times \pi \times 100$

Area of the sector $=3 \times \pi \times 10$

$\Rightarrow$ Area of the sector $=30 \pi$

Therefore, area of the sector is $30 \pi \mathrm{cm}^{2}$.