A hemispherical bowl has internal radius of 6 cm. the internal surface area would be : (Take `pi = 3.14`)

Options

A. `225 cm^(2)`
B. `400 cm^(2)`
C. `289.75 cm^(2)`
D. `226.08 cm^(2)`

Answer

To find the internal surface area of a hemispherical bowl with an internal radius of 6 cm, we can follow these steps:

### Step 1: Identify the formula for the surface area of a hemisphere.
The formula for the curved surface area of a hemisphere is given by:
\[ \text{Curved Surface Area} = 2\pi r^2 \]
where \( r \) is the radius of the hemisphere.

### Step 2: Substitute the given values into the formula.
Here, the internal radius \( r \) is 6 cm. We will substitute this value into the formula:
\[ \text{Curved Surface Area} = 2 \times \pi \times (6)^2 \]

### Step 3: Calculate \( (6)^2 \).
Calculating \( (6)^2 \):
\[ (6)^2 = 36 \]

### Step 4: Substitute \( (6)^2 \) back into the formula.
Now substituting back:
\[ \text{Curved Surface Area} = 2 \times \pi \times 36 \]

### Step 5: Substitute the value of \( \pi \).
Given that \( \pi = 3.14 \), we substitute this value:
\[ \text{Curved Surface Area} = 2 \times 3.14 \times 36 \]

### Step 6: Calculate \( 2 \times 3.14 \).
Calculating \( 2 \times 3.14 \):
\[ 2 \times 3.14 = 6.28 \]

### Step 7: Multiply by 36.
Now we multiply:
\[ \text{Curved Surface Area} = 6.28 \times 36 \]

### Step 8: Perform the final multiplication.
Calculating \( 6.28 \times 36 \):
\[ 6.28 \times 36 = 226.08 \]

### Step 9: State the final answer.
Thus, the internal surface area of the hemispherical bowl is:
\[ \text{Internal Surface Area} = 226.08 \, \text{cm}^2 \]