The volume of a right circular cone is 2464 `cm^(3)`. If the height of cone is 12 cm, then what will be the radius of its base?

Options

A. 12cm
B. 8cm
C. 14cm
D. 10cm

Answer

To find the radius of the base of a right circular cone given its volume and height, we can use the formula for the volume of a cone:

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

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Volume \( V = 2464 \, \text{cm}^3 \)
- Height \( h = 12 \, \text{cm} \)

2. **Substitute the known values into the volume formula**:
\[ 2464 = \frac{1}{3} \pi r^2 (12) \]

3. **Simplify the equation**:
- First, simplify \( \frac{1}{3} \times 12 \):
\[ \frac{1}{3} \times 12 = 4 \]
- Now the equation becomes:
\[ 2464 = 4 \pi r^2 \]

4. **Isolate \( r^2 \)**:
- Divide both sides by \( 4\pi \):
\[ r^2 = \frac{2464}{4\pi} \]

5. **Substitute \( \pi \) with \( \frac{22}{7} \)** (approximation):
\[ r^2 = \frac{2464}{4 \times \frac{22}{7}} = \frac{2464 \times 7}{88} \]

6. **Calculate \( r^2 \)**:
- First, calculate \( 2464 \times 7 \):
\[ 2464 \times 7 = 17248 \]
- Now divide by \( 88 \):
\[ r^2 = \frac{17248}{88} = 196 \]

7. **Find \( r \)**:
- Take the square root of \( r^2 \):
\[ r = \sqrt{196} = 14 \, \text{cm} \]

### Final Answer:
The radius of the base of the cone is \( 14 \, \text{cm} \).