If the diameter of a sphere is 14 cm, then what is the curved surface area (in cm2) of the sphere?

Options

A. 616
B. 1232
C. 2464
D. 576

Answer

To find the curved surface area of a sphere given its diameter, we can follow these steps:

### Step 1: Identify the diameter
The diameter of the sphere is given as 14 cm.

### Step 2: Calculate the radius
The radius (r) of the sphere is half of the diameter.
\[ r = \frac{\text{Diameter}}{2} = \frac{14 \text{ cm}}{2} = 7 \text{ cm} \]

### Step 3: Use the formula for curved surface area
The formula for the curved surface area (CSA) of a sphere is:
\[ \text{CSA} = 4 \pi r^2 \]

### Step 4: Substitute the radius into the formula
Now, substitute the radius into the formula:
\[ \text{CSA} = 4 \pi (7 \text{ cm})^2 \]

### Step 5: Calculate \( r^2 \)
Calculate \( r^2 \):
\[ (7 \text{ cm})^2 = 49 \text{ cm}^2 \]

### Step 6: Substitute \( r^2 \) into the formula
Now substitute \( r^2 \) back into the CSA formula:
\[ \text{CSA} = 4 \pi \times 49 \text{ cm}^2 \]

### Step 7: Calculate the value of \( 4 \times 49 \)
Calculate \( 4 \times 49 \):
\[ 4 \times 49 = 196 \]

### Step 8: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = 196 \times \frac{22}{7} \]

### Step 9: Simplify the expression
Now simplify:
\[ \text{CSA} = 196 \times \frac{22}{7} = \frac{196 \times 22}{7} \]
Calculating \( 196 \div 7 \):
\[ 196 \div 7 = 28 \]
So,
\[ \text{CSA} = 28 \times 22 \]

### Step 10: Calculate the final value
Now calculate \( 28 \times 22 \):
\[ 28 \times 22 = 616 \]

### Final Answer
The curved surface area of the sphere is:
\[ \text{CSA} = 616 \text{ cm}^2 \]