The radius of a hemispherical bowl is 6 cm. The capacity of the bowl is
(Take `pi = (22)/(7)`)

Options

A. `345.53 cm^(3)`
B. `452 cm^(3)`
C. `495.51 cm^(3)`
D. `452.57 cm^(3)`

Answer

To find the capacity of a hemispherical bowl with a radius of 6 cm, we need to calculate the volume of the hemisphere using the formula for the volume of a hemisphere.

### Step-by-Step Solution:

1. **Identify the formula for the volume of a hemisphere**:
The formula for the volume \( V \) of a hemisphere is given by:
\[ V = \frac{2}{3} \pi r^3 \]
where \( r \) is the radius of the hemisphere.

2. **Substitute the given values**:
We are given that the radius \( r = 6 \) cm and \( \pi = \frac{22}{7} \). Now, substitute these values into the formula:
\[ V = \frac{2}{3} \times \frac{22}{7} \times (6)^3 \]

3. **Calculate \( (6)^3 \)**:
First, calculate \( 6^3 \):
\[ 6^3 = 6 \times 6 \times 6 = 216 \]

4. **Substitute \( 216 \) into the volume formula**:
Now substitute \( 216 \) back into the volume formula:
\[ V = \frac{2}{3} \times \frac{22}{7} \times 216 \]

5. **Multiply the constants**:
First, calculate \( \frac{2 \times 22 \times 216}{3 \times 7} \):
\[ V = \frac{2 \times 22 \times 216}{3 \times 7} = \frac{9504}{21} \]

6. **Perform the division**:
Now, divide \( 9504 \) by \( 21 \):
\[ V = 452.57 \, \text{cm}^3 \]

### Final Answer:
The capacity of the hemispherical bowl is \( 452.57 \, \text{cm}^3 \).

---