A solid hemisphere consists of a flat circular base and a curved hemisphere on top of it. To find the total surface area, we need to calculate the area of the curved surface (hemisphere) and the area of the circular base, then add them together.

1. Curved Surface Area of the Hemisphere:

The curved surface area of a hemisphere is half the surface area of a complete sphere with the same radius. The formula for the surface area of a sphere is \(4\pi r^2\), where \(r\) is the radius.

Curved Surface Area of Hemisphere = \(\frac{1}{2} \cdot 4\pi r^2 = 2\pi r^2\).

Plugging in the given radius (\(r = 7\) cm):

Curved Surface Area = \(2\pi \cdot (7 \, \text{cm})^2 = 2\pi \cdot 49 \, \text{cm}^2 = 98\pi \, \text{cm}^2\).

2. Circular Base Area:

The circular base of the hemisphere is a circle with radius \(r\). The formula for the area of a circle is \(\pi r^2\).

Circular Base Area = \(\pi \cdot (7 \, \text{cm})^2 = \pi \cdot 49 \, \text{cm}^2 = 49\pi \, \text{cm}^2\).

Total Surface Area = Curved Surface Area + Circular Base Area:

Total Surface Area = \(98\pi \, \text{cm}^2 + 49\pi \, \text{cm}^2 = 147\pi \, \text{cm}^2\).

Now, let's calculate the approximate numerical value of the total surface area:

Total Surface Area ≈ \(147 \cdot 3.14 \, \text{cm}^2 \approx 462 \, \text{cm}^2\).