What is the formula for finding the surface area of an open cylinder with radius of base 'r' and height 'h'?

Options

A. `2pi r h`
B. `pi r^(2) h`
C. `pi r (2h + r)`
D. `2pi r (h + r)`

Answer

To find the surface area of an open cylinder with a radius of base 'r' and height 'h', we can follow these steps:

### Step-by-Step Solution

1. **Understand the Structure of the Cylinder**:
An open cylinder has one circular base and a curved surface. The top of the cylinder is open.

2. **Calculate the Curved Surface Area**:
The formula for the curved surface area (CSA) of a cylinder is given by:
\[ \text{Curved Surface Area} = 2 \pi r h \]
where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

3. **Calculate the Area of the Base**:
The area of the circular base is calculated using the formula:
\[ \text{Area of Base} = \pi r^2 \]

4. **Combine the Areas**:
Since the cylinder is open at the top, the total surface area (TSA) is the sum of the curved surface area and the area of the base:
\[ \text{Total Surface Area} = \text{Curved Surface Area} + \text{Area of Base} \]
Substituting the formulas we have:
\[ \text{Total Surface Area} = 2 \pi r h + \pi r^2 \]

5. **Factor the Expression**:
We can factor out \( \pi r \) from the expression:
\[ \text{Total Surface Area} = \pi r (2h + r) \]

### Final Formula
Thus, the formula for the surface area of an open cylinder is:
\[ \text{Total Surface Area} = \pi r (2h + r) \]