Find the total surface area of a hemisphere with a radius of 11 cm?

The correct option is $363\pi {\mathrm{cm}}^2$.

Step-by-step Explanation:

1. Formula for Total Surface Area of a Hemisphere:
A hemisphere consists of two surfaces:

• The curved surface area, which is given by $2\pi r^2$
• The flat circular base, which has an area of $\pi r^2$

Adding these two areas together gives the formula for the total surface area (TSA) of a solid hemisphere:

$\text{Total Surface Area (TSA)}=2\pi r^2+\pi r^2=3\pi r^2$

2. Substitute the Given Values:
We are given that the radius of the hemisphere, $r=11 \text{cm}$.

Substitute $r=11$ into the total surface area formula:

$\text{TSA}=3\times \pi \times {\left(11\right)}^2$

3. Calculate the Final Value:

${11}^2=121$

$\text{TSA}=3\times 121\times \pi =363\pi {\text{cm}}^2$

Therefore, the total surface area of the hemisphere is $363\pi {\mathrm{cm}}^2$.