The inner curved surface area of a hollow hemispherical bowl of external radius 14 cm and thickness 2 cm is ______.

Answer

To find the inner curved surface area of a hollow hemispherical bowl with an external radius of 14 cm and a thickness of 2 cm, we can follow these steps:

### Step 1: Determine the inner radius
The external radius of the bowl is given as 14 cm, and the thickness of the bowl is 2 cm. To find the inner radius, we subtract the thickness from the external radius.

\[ \text{Inner radius} = \text{External radius} - \text{Thickness} = 14 \, \text{cm} - 2 \, \text{cm} = 12 \, \text{cm} \]

### Step 2: Use the formula for the curved surface area of a hemisphere
The formula for the curved surface area (CSA) of a hemisphere is given by:

\[ \text{CSA} = 2\pi r^2 \]

where \( r \) is the radius of the hemisphere.

### Step 3: Substitute the inner radius into the formula
Now, we substitute the inner radius (12 cm) into the formula:

\[ \text{CSA} = 2\pi (12)^2 \]

### Step 4: Calculate \( (12)^2 \)
Calculating \( (12)^2 \):

\[ (12)^2 = 144 \]

### Step 5: Substitute back into the CSA formula
Now, substitute \( 144 \) back into the CSA formula:

\[ \text{CSA} = 2\pi \times 144 \]

### Step 6: Multiply by 2
Now, calculate \( 2 \times 144 \):

\[ 2 \times 144 = 288 \]

### Step 7: Write the final expression for the CSA
Thus, the inner curved surface area becomes:

\[ \text{CSA} = 288\pi \, \text{cm}^2 \]

### Final Answer
The inner curved surface area of the hollow hemispherical bowl is \( 288\pi \, \text{cm}^2 \).

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