If the total suface area of a hemisphere is 27` pi` square cm, then the radius of the base of the hemisphere is

Options

A. `9sqrt3` cm
B. 3 cm
C. `3sqrt3`
D. 9 cm

Answer

To find the radius of the base of the hemisphere given its total surface area, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the total surface area of a hemisphere:**
The total surface area (TSA) of a hemisphere is given by the formula:
\[ \text{TSA} = 3\pi r^2 \]
where \( r \) is the radius of the hemisphere.

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

3. **Simplify the equation:**
We can divide both sides of the equation by \( \pi \) (since \( \pi \) is common on both sides and is not zero):
\[ 3r^2 = 27 \]

4. **Isolate \( r^2 \):**
Now, divide both sides by 3 to isolate \( r^2 \):
\[ r^2 = \frac{27}{3} \]
\[ r^2 = 9 \]

5. **Find the radius \( r \):**
To find \( r \), take the square root of both sides:
\[ r = \sqrt{9} \]
\[ r = 3 \]

6. **Conclusion:**
Therefore, the radius of the base of the hemisphere is \( 3 \) cm.

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

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