Find total surface area of a solid hemi-sphere of radius 7cm.

Answer

To find the total surface area of a solid hemisphere with a radius of 7 cm, we will follow these steps:

### Step 1: Understand the Components of the Total Surface Area
The total surface area (TSA) of a solid hemisphere consists of two parts:
1. The curved surface area (CSA)
2. The area of the circular base

### Step 2: Use the Formulas
The formulas we need are:
- Curved Surface Area (CSA) of a hemisphere: \( CSA = 2\pi r^2 \)
- Area of the circular base: \( A = \pi r^2 \)

### Step 3: Calculate the Curved Surface Area
Using the radius \( r = 7 \) cm:
\[ CSA = 2\pi r^2 = 2\pi (7)^2 = 2\pi (49) = 98\pi \text{ cm}^2 \]

### Step 4: Calculate the Area of the Base
Using the same radius:
\[ A = \pi r^2 = \pi (7)^2 = \pi (49) = 49\pi \text{ cm}^2 \]

### Step 5: Add Both Areas to Find Total Surface Area
Now, we can find the total surface area:
\[ TSA = CSA + A = 98\pi + 49\pi = 147\pi \text{ cm}^2 \]

### Step 6: Substitute the Value of \(\pi\)
For calculation, we can use \(\pi \approx \frac{22}{7}\):
\[ TSA = 147 \times \frac{22}{7} \text{ cm}^2 \]

### Step 7: Perform the Calculation
Calculating the above expression:
\[ TSA = 147 \times \frac{22}{7} = 147 \times 3.14 = 462 \text{ cm}^2 \]

### Final Answer
The total surface area of the solid hemisphere is \( 462 \text{ cm}^2 \).

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