Find the radius of the sphere whose curved surface area is `64pi Cm^2`

Options

A. `8 cm`
B. `4 cm`
C. `3cm`
D. `2cm`

Answer

To find the radius of the sphere whose curved surface area is \(64\pi \, \text{cm}^2\), we can follow these steps:

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

### Step 2: Set the curved surface area equal to the given value.
According to the problem, the curved surface area 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 simplify the equation by dividing both sides by \(\pi\):
\[ 4r^2 = 64 \]

### Step 4: Divide both sides by 4.
Next, we divide both sides by 4 to isolate \(r^2\):
\[ r^2 = \frac{64}{4} = 16 \]

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

### Conclusion
The radius of the sphere is \(4 \, \text{cm}\).

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