How To Find The Surface Area Of An Oblique Cylinder

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.