Surface area of a cylinder

- To determine the area of a given cylinder.
- To obtain the formula for the lateral surface area of a right circular cylinder in terms of the radius(r) of its base and height (h).

**Definition**: A right circular cylinder is a three-dimensional object with two congruent circles as parallel bases and a lateral surface consisting of a rectangle.

**Base and side:** The bases of right circular cylinder are always congruent and parallel to each other. If you were to 'unroll' the cylinder you would find the side is actually a rectangle when flattened out.

**Height:** The height **h** is the perpendicular distance between the bases.

**Radius:** The radius **r** of a cylinder is the radius of a base.

To find the surface area of a cylinder add curved (lateral) surface area and area of both bases.

**Area of both bases** - Each base is a circle so the area of each base is **πr²**, where **r** is the radius of the base. There are two bases so their combined surface area is **2 X πr²**.

**Curved Surface Area** - As mentioned above the surface area of the cylinder opens to form a rectangular region. Breadth of this rectangle in height of the cylinder i.e **h** and Length of the rectangle is circumference of the base of the cylinder i.e. **2πr**. Hence area of curved surface area - **2πr X h**

Total surface area of cylinder = curved surface area (c) + 2 (area of base circle)

= 2.π.r.h + 2.π.r²

= 2.π.r (h + r)

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