The volume of a sphere is `(88)/(21) xx (14)^(3) cm^(3)`. The curved surface of the sphere is (Take `pi = (22)/(7)`)

Options

A. `2424 cm^(2)`
B. `2446 cm^(2)`
C. `2484 cm^(2)`
D. `2464 cm^(2)`

Answer

To find the curved surface area of the sphere given its volume, we will follow these steps:

### Step 1: Write down the formula for the volume of a sphere.
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]

### Step 2: Substitute the given volume into the formula.
We are given that the volume of the sphere is:
\[ V = \frac{88}{21} \times 14^3 \text{ cm}^3 \]
So, we can set up the equation:
\[ \frac{4}{3} \pi r^3 = \frac{88}{21} \times 14^3 \]

### Step 3: Substitute the value of \( \pi \).
We are instructed to take \( \pi = \frac{22}{7} \). Substituting this into the equation gives:
\[ \frac{4}{3} \times \frac{22}{7} \times r^3 = \frac{88}{21} \times 14^3 \]

### Step 4: Simplify the equation.
First, simplify the left side:
\[ \frac{88}{21} \times r^3 = \frac{88}{21} \times 14^3 \text{ (after multiplying both sides by } \frac{3}{4} \text{ and } \frac{7}{22}) \]

### Step 5: Cancel out \( \frac{88}{21} \).
Since \( \frac{88}{21} \) is on both sides, we can cancel it out:
\[ r^3 = 14^3 \]

### Step 6: Take the cube root to find \( r \).
Taking the cube root of both sides, we find:
\[ r = 14 \text{ cm} \]

### Step 7: Calculate the curved surface area.
The formula for the curved surface area \( A \) of a sphere is:
\[ A = 4 \pi r^2 \]
Substituting \( r = 14 \) cm and \( \pi = \frac{22}{7} \):
\[ A = 4 \times \frac{22}{7} \times (14)^2 \]

### Step 8: Calculate \( (14)^2 \).
Calculating \( (14)^2 \):
\[ (14)^2 = 196 \]

### Step 9: Substitute back into the area formula.
Now substituting back:
\[ A = 4 \times \frac{22}{7} \times 196 \]

### Step 10: Simplify the expression.
Calculating \( 4 \times 196 = 784 \):
\[ A = \frac{22 \times 784}{7} \]

### Step 11: Divide \( 784 \) by \( 7 \).
Calculating \( \frac{784}{7} = 112 \):
\[ A = 22 \times 112 \]

### Step 12: Final multiplication.
Calculating \( 22 \times 112 = 2464 \):
\[ A = 2464 \text{ cm}^2 \]

### Conclusion:
The curved surface area of the sphere is \( 2464 \text{ cm}^2 \).