# Cylinder Area Calculator

## Area

## Cylinder

## Cylinder area

A cylinder is a three-dimensional shape with a circular base and a curved surface that extends up from the base to a flat top. To calculate the area of a cylinder, you'll need to use the formula that corresponds to the part of the cylinder you're measuring. The area of the base is given by the formula for the area of a circle, while the lateral surface area and the total surface area require different formulas.

## Cylinder Area Formulas

### Lateral Surface Area

The formula for the lateral surface area of a cylinder is:

S = 2\pi rh

where r is the radius of the circular base and h is the height of the cylinder. This formula gives you the surface area of the curved part of the cylinder. It comes from the fact that the lateral surface of a cylinder can be `unrolled` to form a rectangle with a length of the circumference of the base (2πr) and a height of the height of the cylinder (h).

### Total Surface Area

The formula for the total surface area of a cylinder is:

S = 2\pi r(h+r)

This formula gives you the sum of the areas of the curved surface and the two circular bases of the cylinder. It comes from adding the area of the base to the lateral surface area.

## Using the Cylinder Area Calculator

Our cylinder area calculator makes it easy to find the area of your cylinder. To use the calculator:

- Select the type of surface area you want to calculate (lateral surface area or total surface area) from the drop-down menu.
- Enter the radius of the base in the first box.
- Enter the height of the cylinder in the second box.
- Our calculator will automatically calculate the area of your cylinder.

Our calculator will give you the lateral, and the total surface area of your cylinder.

## Example

For example, let's say you have a cylinder with a radius of 5 cm and a height of 10 cm. To find the area of the base, use the formula for the area of a circle:

\text{Area of Base} = \pi r^2 = \pi 5^2 = 25\pi cm

To find the lateral surface area, use the formula for the lateral surface area of a cylinder:

\ ext{Lateral Surface Area} = 2\pi r h = 2*5*10\pi = 100\pi cm

To find the total surface area, use the formula for the total surface area of a cylinder:

\ ext{Total Surface Area} = 2\pi r(h+r) = 2\pi 5 (10+5)= 150 \pi cm

## Conclusion

Calculating the surface area of a cylinder is an important skill in geometry. Our cylinder area calculator and formulas make it easy to find the surface area of your cylinder. Try it out for yourself and see how easy it can be!

- Area
- Volume
- Perimeter
- Side
- Height
- Diagonal
- Radius
- Median
- Bisector
- Angle
- Theorems