If the volume of a sphere is `4851 cm^3`, then its surface area (in `cm^2`) is: यदि एक गोले का आयतन `4851 cm^3` है, तो इसका क्षेत्रफल (`cm^2` में) है: (take `pi= 22/7`)

Options

A. 1323
B. 2772
C. 1337
D. 1386

Answer

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

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

### Step 2: Set the volume equal to the given value.
We know the volume of the sphere is \( 4851 \, \text{cm}^3 \). Thus, we can set up the equation:
\[ \frac{4}{3} \pi r^3 = 4851 \]

### Step 3: Substitute the value of \( \pi \).
Using \( \pi = \frac{22}{7} \), we substitute this into the equation:
\[ \frac{4}{3} \cdot \frac{22}{7} \cdot r^3 = 4851 \]

### Step 4: Solve for \( r^3 \).
First, multiply both sides by \( \frac{3}{4} \):
\[ \frac{22}{7} r^3 = 4851 \cdot \frac{3}{4} \]
Calculating the right side:
\[ 4851 \cdot \frac{3}{4} = 3638.25 \]
Now, multiply both sides by \( \frac{7}{22} \):
\[ r^3 = 3638.25 \cdot \frac{7}{22} \]
Calculating this gives:
\[ r^3 = \frac{25467.75}{22} = 1153.125 \]

### Step 5: Find the cube root of \( r^3 \).
To find \( r \), we take the cube root of \( 1153.125 \):
\[ r = \sqrt[3]{1153.125} \approx 10.5 \, \text{cm} \]

### Step 6: Write down the formula for the surface area of a sphere.
The formula for the surface area \( A \) of a sphere is:
\[ A = 4 \pi r^2 \]

### Step 7: Substitute the value of \( r \) into the surface area formula.
Substituting \( r \approx 10.5 \, \text{cm} \) and \( \pi = \frac{22}{7} \):
\[ A = 4 \cdot \frac{22}{7} \cdot (10.5)^2 \]

### Step 8: Calculate \( (10.5)^2 \).
Calculating \( (10.5)^2 \):
\[ (10.5)^2 = 110.25 \]

### Step 9: Substitute and calculate the surface area.
Now substituting back into the surface area formula:
\[ A = 4 \cdot \frac{22}{7} \cdot 110.25 \]
Calculating:
\[ A = \frac{88}{7} \cdot 110.25 = \frac{9684}{7} \approx 1383.43 \, \text{cm}^2 \]

### Final Answer:
Thus, the surface area of the sphere is approximately \( 1386 \, \text{cm}^2 \).

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