Find the volume of the right circular cone with radius 3.5 cm & height 12 cm ?

Options

A. `308 cm^3`
B. `154 cm^3`
C. `77 cm^3`
D. `231 cm^3`

Answer

To find the volume of a right circular cone, we can use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius \( r = 3.5 \) cm
- Height \( h = 12 \) cm

2. **Convert the radius into a fraction**:
- \( r = 3.5 \) cm can be expressed as \( \frac{7}{2} \) cm.

3. **Substitute the values into the volume formula**:
\[ V = \frac{1}{3} \pi \left(\frac{7}{2}\right)^2 (12) \]

4. **Calculate \( r^2 \)**:
\[ \left(\frac{7}{2}\right)^2 = \frac{49}{4} \]

5. **Substitute \( r^2 \) back into the volume formula**:
\[ V = \frac{1}{3} \pi \left(\frac{49}{4}\right) (12) \]

6. **Multiply \( \frac{49}{4} \) by \( 12 \)**:
\[ \frac{49 \times 12}{4} = \frac{588}{4} = 147 \]

7. **Now substitute this back into the volume formula**:
\[ V = \frac{1}{3} \pi (147) \]

8. **Use \( \pi \approx \frac{22}{7} \)** for calculation**:
\[ V = \frac{1}{3} \times \frac{22}{7} \times 147 \]

9. **Calculate \( \frac{22 \times 147}{21} \)**:
- First, simplify:
\[ 147 \div 21 = 7 \]
- Then calculate:
\[ V = \frac{22 \times 7}{1} = 154 \text{ cm}^3 \]

### Final Answer:
The volume of the right circular cone is \( 154 \text{ cm}^3 \).