## How to Find the Surface Area of a Cylinder

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### Definition

A cylinder is a frequently seen three-dimensional solid in our environment, such as a glue stick for crafts, a soft drink that can satisfy our thirst, or a remote control battery. Taking a look at these things we see every day, we can say that a cylinder has two **circular** bases, one at the top and one at the bottom. These two bases are circles that look and are the **same** size and shape. Line segments **connect** these two bases, giving the cylinder its shape.

### What is the Area of Surface?

The surface area is the amount of **space** that a three-dimensional object takes up on the **outside**. This idea is **different** from the definition of the area because the area is used to describe **two-dimensional** things. The surface area of a cylinder is the **sum** of its three parts, which are two **circular** bases and a **side**.

### What does LSA stand for?

The part of a three-dimensional object that is **not** the base is called the **lateral** surface area. In a cylinder, the two bases are parallel circles joined by parts of the line that make up the cylinder's side. If you draw this part of the cylinder on a flat surface, it looks like a **rectangle** with a **height** equal to the height of the cylinder and a **width** equal to the sum of the **circumferences** of the bases.

### How to Find the Area of a Cylinder's Surface

Think about a cylinder whose height is \(h\) and whose base radius is \(r\). The formula for finding a cylinder's surface area is:

\(A \ = \ 2πr^2h \ + \ 2πrh\)

The **first** term gives the surface area of the **two** bases and the **second** term gives the surface area of the cylinder's **side**. When doing this kind of evaluation, a cylinder **unit's** surface area must be kept in mind. The radius and the height must be given in the **same** unit, and the surface area will be the **square** of this unit. For example, if the height and radius of the bases are given in centimeters, the surface area will be given in centimeters squared.

### Example:

Figure out how much it will cost to paint a right circular cylinder with a base radius of \(6\) meters and a height of \(17\) meters. If the cost of painting the container is INR \(4\) per square meter. (Take \(π \ = \ 3.14\))

**Solution:**

Total surface area of cylinder \(= \ 2πr \ (h \ + \ r) \ = \ 2(3.14)(6)(17 \ + \ 6) \ = \ 866.64\)m\(^2\)

The cost to paint the cylinder is \(4\) per square meter: Total cost of painting \(= \ 4 \times 866.64 \ = \ 3466.56\)

### Exercises for Surface Area of a Cylinder

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## Surface Area of a Cylinder Practice Quiz

### More Solid Figures courses

- How to Find the Volume of a Rectangular Prism
- How to Find the Volume of a Cylinder
- How to Find the Surface Area of a Cylinder
- How to Find the Surface Area of a Rectangular Prism
- How to Find Volume and Surface Area of Cubes
- How to Find the Volume of a Cube
- How to Find Volume and Surface Area of Pyramids and Cone