The diameter of base of a right circular cone is 7 cm and slant height is 10 cm, then what is its lateral surface area?

Options

A. 110 sq cm
B. 100 sq cm
C. 70 sq cm
D. 49 sq cm

Answer

To find the lateral surface area of a right circular cone, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Diameter of the base of the cone (D) = 7 cm
- Slant height of the cone (L) = 10 cm

2. **Calculate the radius of the base**:
- The radius (R) is half of the diameter.
\[ R = \frac{D}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} \]

3. **Use the formula for lateral surface area of a cone**:
- The formula for the lateral surface area (A) of a cone is:
\[ A = \pi R L \]
where \( \pi \) is approximately \( \frac{22}{7} \).

4. **Substitute the values into the formula**:
\[ A = \frac{22}{7} \times R \times L \]
Substituting the values of \( R \) and \( L \):
\[ A = \frac{22}{7} \times 3.5 \text{ cm} \times 10 \text{ cm} \]

5. **Simplify the expression**:
- First, calculate \( \frac{22}{7} \times 3.5 \):
\[ \frac{22}{7} \times 3.5 = \frac{22 \times 3.5}{7} = \frac{77}{7} = 11 \]
- Now substitute back into the area formula:
\[ A = 11 \times 10 = 110 \text{ cm}^2 \]

6. **Conclusion**:
- The lateral surface area of the cone is \( 110 \text{ cm}^2 \).

### Final Answer:
The lateral surface area of the cone is \( 110 \text{ cm}^2 \).

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