To find the total surface area of a solid hemisphere, we need to consider both the curved surface area and the flat circular base of the hemisphere.

Step-by-Step Solution

1. Curved Surface Area of Hemisphere:

   The formula for the curved surface area of a hemisphere is:

   $\text{Curved Surface Area} = 2 \pi r^2$

2. Area of the Base:

   The base of the hemisphere is a circle with the same radius $r$. The area of the base is:

   $\text{Base Area} = \pi r^2$

3. Total Surface Area of the Hemisphere:

   The total surface area is the sum of the curved surface area and the base area:

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

   Now, substitute the given values:

   $r = 7 \, \text{cm}, \quad \pi = 3.142$

   So,

   $\text{Total Surface Area} = 3 \times 3.142 \times (7)^2$

   Calculate $7^2$:

   $7^2 = 49$

   Now substitute this value:

   $\text{Total Surface Area} = 3 \times 3.142 \times 49$

   Compute the multiplication:

   $\text{Total Surface Area} = 3 \times 154.958 = 464.874 \, \text{cm}^2$

Final Answer

The total surface area of the solid hemisphere is 464.874 cm².

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the surface area change if the radius were doubled?
2. What is the volume of a hemisphere with the same radius?
3. How do you find the surface area of a hollow hemisphere?
4. How does the use of different values for $\pi$ affect the calculation?
5. Can you derive the formula for the surface area of a hemisphere from scratch?

Tip: Remember that for surface area calculations, always double-check which parts of the solid are included (like bases or curves) in the final measurement.