The surface area of a sphere is `64 pi cm^(2)`. Its diameter is equal to

Options

A. a)16 cm
B. b)8 cm
C. c)4 cm
D. d)2 cm

Answer

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

### Step 1: Understand 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: Set up the equation using the given surface area.
We know the surface area of the sphere is \( 64 \pi \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 4 \pi r^2 = 64 \pi \]

### Step 3: Simplify the equation.
We can divide both sides of the equation by \( \pi \):
\[ 4 r^2 = 64 \]

### Step 4: Solve for \( r^2 \).
Now, divide both sides by 4:
\[ r^2 = \frac{64}{4} = 16 \]

### Step 5: Find the radius \( r \).
To find \( r \), take the square root of both sides:
\[ r = \sqrt{16} = 4 \, \text{cm} \]

### Step 6: Calculate the diameter \( d \).
The diameter \( d \) of the sphere is twice the radius:
\[ d = 2r = 2 \times 4 = 8 \, \text{cm} \]

### Final Answer:
The diameter of the sphere is \( 8 \, \text{cm} \).

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