To find the lateral surface area of a cylinder, use the formula:
Lateral Surface Area=2πrh\text{Lateral Surface Area}=2\pi rhLateral Surface Area=2πrh
where:
- rrr is the radius of the circular base of the cylinder,
- hhh is the height of the cylinder,
- π\pi π (pi) is approximately 3.14 or 227\frac{22}{7}722.
Explanation:
The lateral surface area corresponds to the curved surface that wraps around the cylinder, excluding the top and bottom circular bases. If you "unwrap" this curved surface, it forms a rectangle where:
- The length of the rectangle is the circumference of the base circle, 2πr2\pi r2πr,
- The width of the rectangle is the height hhh.
Multiplying these gives the lateral surface area formula:
Lateral Surface Area=circumference×height=2πr×h\text{Lateral Surface Area}=\text{circumference}\times \text{height}=2\pi r\times hLateral Surface Area=circumference×height=2πr×h
Example:
If a cylinder has a diameter of 10 cm and a height of 12 cm:
- Radius r=102=5r=\frac{10}{2}=5r=210=5 cm,
- Height h=12h=12h=12 cm,
- Lateral surface area =2π×5×12=120π≈377 cm2=2\pi \times 5\times 12=120\pi \approx 377\text{ cm}^2=2π×5×12=120π≈377 cm2.
This formula provides the curved surface area without including the areas of the circular top and bottom bases
