Find the total surface area of a hemisphere of radius `21cm`.

Options

A. `4158 cm^2`
B. `3500 cm^2`
C. `4000 cm^2`
D. None of above

Explanation

To find the total surface area of a hemisphere with a radius of 21 cm, we can follow these steps:

### Step 1: Understand the formula for the total surface area of a hemisphere.
The total surface area (TSA) of a hemisphere is given by the formula:
\[ \text{TSA} = 3\pi r^2 \]
where \( r \) is the radius of the hemisphere.

### Step 2: Substitute the radius into the formula.
Given that the radius \( r = 21 \) cm, we can substitute this value into the formula:
\[ \text{TSA} = 3\pi (21)^2 \]

### Step 3: Calculate \( (21)^2 \).
First, calculate the square of the radius:
\[ (21)^2 = 441 \]

### Step 4: Substitute \( 441 \) back into the formula.
Now substitute \( 441 \) back into the TSA formula:
\[ \text{TSA} = 3\pi \times 441 \]

### Step 5: Use the approximation \( \pi \approx \frac{22}{7} \).
Now, we can use the approximation for \( \pi \):
\[ \text{TSA} = 3 \times \frac{22}{7} \times 441 \]

### Step 6: Calculate \( 3 \times \frac{22}{7} \).
First, calculate \( 3 \times 22 = 66 \):
\[ \text{TSA} = \frac{66}{7} \times 441 \]

### Step 7: Simplify \( \frac{441}{7} \).
Now, divide \( 441 \) by \( 7 \):
\[ 441 \div 7 = 63 \]
So, we have:
\[ \text{TSA} = 66 \times 63 \]

### Step 8: Calculate \( 66 \times 63 \).
Now, multiply \( 66 \) by \( 63 \):
\[ 66 \times 63 = 4158 \]

### Step 9: Write the final answer with the correct units.
Thus, the total surface area of the hemisphere is:
\[ \text{TSA} = 4158 \, \text{cm}^2 \]

### Summary of the Solution:
The total surface area of a hemisphere with a radius of 21 cm is \( 4158 \, \text{cm}^2 \).

---