Determining the surface area of a cylinder is a common task in geometry. This guide will provide a step-by-step process to find the surface area of a cylinder using its radius and height.
Step 1: Show the Surface Area Formula
The formula for the surface area \(SA\) of a cylinder is:
\[ SA = 2 \cdot \pi \cdot r \cdot (h + r) \]
Where:
- \(r\) is the radius of the cylinder.
- \(h\) is the height of the cylinder.
Step 2: Explain the Formula
In this formula:
- \(2 \cdot \pi \cdot r \cdot h\) represents the lateral surface area of the 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 a cylinder with:
- Radius \(r = 5\) units
- Height \(h = 10\) units
Step 4: Calculate the Final Value
First, we substitute the values into the formula:
\[ SA = 2 \cdot \pi \cdot 5 \cdot (10 + 5) \]
Next, we simplify inside the parentheses:
\[ SA = 2 \cdot \pi \cdot 5 \cdot 15 \]
Now, multiply the numbers:
\[ SA = 2 \cdot \pi \cdot 75 \]
\[ SA = 150 \cdot \pi \]
For \(\pi \approx 3.14\):
\[ SA \approx 150 \cdot 3.14 \]
\[ SA \approx 471 \, \text{square units} \]
Final Value
The surface area of a cylinder with a radius of 5 units and a height of 10 units is approximately 471 square units.
