Find the curved surface area (in `cm^2` ) of a hemisphere of diameter 28 cm.

Options

A. 1152
B. 1024
C. 956
D. 1232

Answer

To find the curved surface area of a hemisphere with a diameter of 28 cm, we will follow these steps:

### Step 1: Find the radius of the hemisphere.
The radius \( r \) is half of the diameter.

\[ r = \frac{\text{Diameter}}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm} \]

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

\[ A = 2 \pi r^2 \]

### Step 3: Substitute the value of the radius into the formula.
Now we will substitute \( r = 14 \text{ cm} \) into the formula:

\[ A = 2 \pi (14 \text{ cm})^2 \]

### Step 4: Calculate \( r^2 \).
First, we calculate \( r^2 \):

\[ r^2 = 14 \text{ cm} \times 14 \text{ cm} = 196 \text{ cm}^2 \]

### Step 5: Substitute \( r^2 \) back into the formula.
Now we can substitute \( r^2 \) into the formula for the curved surface area:

\[ A = 2 \pi (196 \text{ cm}^2) \]

### Step 6: Use the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \):

\[ A = 2 \times \frac{22}{7} \times 196 \text{ cm}^2 \]

### Step 7: Simplify the expression.
First, calculate \( 2 \times 22 = 44 \):

\[ A = \frac{44}{7} \times 196 \text{ cm}^2 \]

Now, we can simplify \( 196 \div 7 = 28 \):

\[ A = 44 \times 28 \text{ cm}^2 \]

### Step 8: Calculate the final area.
Now calculate \( 44 \times 28 \):

\[ A = 1232 \text{ cm}^2 \]

### Final Answer:
The curved surface area of the hemisphere is \( 1232 \text{ cm}^2 \).

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