If the lateral surface area of a cylinder is 94.2 sq cm and its height is 5 cm, then find the radius of its base. (`pi` = 3.14)

Options

A. 5cm
B. 8 cm
C. 3 cm
D. 4 cm

Answer

To find the radius of the base of the cylinder given the lateral surface area and height, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Lateral Surface Area**:
The lateral surface area (LSA) of a cylinder is given by the formula:
\[ \text{LSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

2. **Substitute the Given Values**:
We know the lateral surface area is \( 94.2 \, \text{cm}^2 \) and the height \( h \) is \( 5 \, \text{cm} \). We also know \( \pi = 3.14 \). Plugging these values into the formula gives:
\[ 94.2 = 2 \times 3.14 \times r \times 5 \]

3. **Simplify the Equation**:
First, calculate \( 2 \times 3.14 \times 5 \):
\[ 2 \times 3.14 = 6.28 \]
\[ 6.28 \times 5 = 31.4 \]
So the equation becomes:
\[ 94.2 = 31.4 \times r \]

4. **Solve for the Radius \( r \)**:
To find \( r \), divide both sides of the equation by \( 31.4 \):
\[ r = \frac{94.2}{31.4} \]

5. **Calculate the Value**:
Performing the division:
\[ r = 3 \]

6. **Conclusion**:
The radius of the base of the cylinder is \( 3 \, \text{cm} \).