The surface area of a sphere is `5544 cm^2`. Find its diameter (in cm).

Options

A. 42
B. 21
C. 84
D. 63

Answer

To find 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 surface area \( A \) of a sphere is given by the formula:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.

### Step 2: Substitute the given surface area into the formula.
We know the surface area \( A \) is \( 5544 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 5544 = 4\pi r^2 \]

### Step 3: Solve for \( r^2 \).
To isolate \( r^2 \), we can rearrange the equation:
\[ r^2 = \frac{5544}{4\pi} \]

### Step 4: Calculate \( r^2 \).
Now we need to calculate \( r^2 \):
\[ r^2 = \frac{5544}{4\pi} \]
Using \( \pi \approx 3.14 \):
\[ r^2 = \frac{5544}{4 \times 3.14} = \frac{5544}{12.56} \approx 441 \]

### Step 5: Find \( r \) by taking the square root of \( r^2 \).
Now, we take the square root of \( 441 \):
\[ r = \sqrt{441} = 21 \, \text{cm} \]

### Step 6: Calculate the diameter.
The diameter \( d \) of the sphere is twice the radius:
\[ d = 2r = 2 \times 21 = 42 \, \text{cm} \]

### Final Answer:
The diameter of the sphere is \( 42 \, \text{cm} \).

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