If the total surface area of a hemisphere is `27 pi` square cm, then the radius of the base of the hemisphere is.
यदि किसी गोलार्द्ध का कुल पृष्ठीय क्षेत्रफल 277 वर्ग सेमी. है, तो गोलार्द्ध के आधार की त्रिज्या है -
A)9 सेमी.
B)`9sqrt(3)` सेमी.
C)3 सेमी.
D)`3sqrt(5)` सेमी.

Options

A. 9 सेमी.
B. `9sqrt(3)` सेमी.
C. 3 सेमी.
D. `3sqrt(5)` सेमी.

Explanation

To find the radius of the base of a hemisphere given that its total surface area is \(27\pi\) square cm, we can follow these steps:

### Step 1: Understand the formula for the total surface area of a hemisphere.
The total surface area \(A\) of a hemisphere is given by the formula:
\[ A = 3\pi r^2 \]
where \(r\) is the radius of the base of the hemisphere.

### Step 2: Set up the equation with the given total surface area.
According to the problem, the total surface area is \(27\pi\) square cm. Therefore, we can set up the equation:
\[ 3\pi r^2 = 27\pi \]

### Step 3: Simplify the equation.
We can divide both sides of the equation by \(\pi\) (since \(\pi\) is a common factor and not equal to zero):
\[ 3r^2 = 27 \]

### Step 4: Solve for \(r^2\).
Next, we divide both sides by 3:
\[ r^2 = \frac{27}{3} = 9 \]

### Step 5: Find the radius \(r\).
Now, we take the square root of both sides to find \(r\):
\[ r = \sqrt{9} = 3 \text{ cm} \]

### Conclusion:
The radius of the base of the hemisphere is \(3\) cm.

### Answer:
The correct option is C) \(3\) cm.

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