The total surface area of a hemisphere is $41.58\text{ sq cm}$. Find its radius.

The formula for the total surface area (TSA) of a solid hemisphere is:
$$\text{TSA}=3\pi r^2$$
Given that $\text{TSA}=41.58{\text{ cm}}^2$, we substitute the values:
$$3\times \frac{22}{7}\times r^2=41.58$$
$$\frac{66}{7}\times r^2=41.58$$
$$r^2=41.58\times \frac{7}{66}$$
$$r^2=0.63\times 7$$
$$r^2=4.41$$
$$r=\sqrt{4.41}=2.1\text{ cm}$$
Thus, the radius of the hemisphere is $2.1\text{ cm}$.