The surface area of a sphere is `2464 cm^2` . Find its diameter (in cm).

Options

A. A) 14
B. B) 56
C. C) 28
D. D) 42

Answer

To solve the problem of finding the diameter of a sphere given its surface area, we can follow these steps:

### Step 1: Write down the formula for the surface area of a sphere.
The formula for the surface area \( A \) of a sphere is given by:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.

### Step 2: Substitute the given surface area into the formula.
We are given that the surface area \( A = 2464 \, \text{cm}^2 \). Substituting this value into the formula, we have:
\[ 2464 = 4\pi r^2 \]

### Step 3: Solve for \( r^2 \).
To isolate \( r^2 \), we first divide both sides by \( 4\pi \):
\[ r^2 = \frac{2464}{4\pi} \]
Using \( \pi \approx \frac{22}{7} \), we can substitute this value in:
\[ r^2 = \frac{2464}{4 \times \frac{22}{7}} = \frac{2464 \times 7}{88} \]

### Step 4: Calculate \( r^2 \).
Now, we simplify the calculation:
\[ r^2 = \frac{2464 \times 7}{88} = \frac{17248}{88} = 196 \]

### Step 5: Find the radius \( r \).
To find \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{196} = 14 \, \text{cm} \]

### Step 6: Calculate the diameter \( d \).
The diameter \( d \) of the sphere is given by:
\[ d = 2r = 2 \times 14 = 28 \, \text{cm} \]

### Final Answer:
The diameter of the sphere is \( 28 \, \text{cm} \).

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