Finding the surface area of an oblique cylinder involves using its radius and slant height. This guide will provide a step-by-step process to determine the surface area using a specific formula.
Step 1: Show the Surface Area Formula
The formula for the surface area \(SA\) of an oblique cylinder is:
\[ SA = 2 \cdot \pi \cdot r \cdot (h_s + r) \]
Where:
- \(r\) is the radius of the base of the cylinder.
- \(h_s\) is the slant height of the cylinder.
Step 2: Explain the Formula
In this formula:
- \(2 \cdot \pi \cdot r \cdot h_s\) represents the lateral surface area of the oblique cylinder.
- \(2 \cdot \pi \cdot r^2\) represents the area of the two circular bases.
The total surface area is the sum of the lateral surface area and the area of the two bases.
Step 3: Insert Numbers as an Example
Let's consider an oblique cylinder with:
- Radius \(r = 4\) units
- Slant height \(h_s = 9\) units
Step 4: Calculate the Final Value
First, we substitute the values into the formula:
\[ SA = 2 \cdot \pi \cdot 4 \cdot (9 + 4) \]
Next, we simplify inside the parentheses:
\[ SA = 2 \cdot \pi \cdot 4 \cdot 13 \]
Now, multiply the numbers:
\[ SA = 2 \cdot \pi \cdot 52 \]
\[ SA = 104 \cdot \pi \]
For \(\pi \approx 3.14\):
\[ SA \approx 104 \cdot 3.14 \]
\[ SA \approx 326.56 \, \text{square units} \]
Final Value
The surface area of an oblique cylinder with a radius of 4 units and a slant height of 9 units is approximately 326.56 square units.
