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**Curved
Surface Area of Cylinder**

The total area around the curved part of a cylinder is
called the

**curved surface area**(CSA) of the cylinder. The curved surface area (CSA) of a cylinder is given by the product of its circumference of circular base (2πr) and height (h) of the cylinder i.e.**CSA = 2πrh**.
This formula can be
understood and derived by the following activities.

Let, the cylinder be hollow and made up of thin sheet of
paper (or metal). If we cut the curved surface along the height AB and unfold it,
then the thin sheet takes the shape of a rectangle ABCD.

The segment DC is coincident with the segment AB when the
sheet was not unfolded. The length of AB = h, the height of the cylinder. The
length of AD = circumference of the upper circular end = 2πr.

Hence, the curved surface area (CSA) of the cylinder =
area of the rectangle ABCD

= AD × AB

= 2πr × h

= 2πrh

*∴*

*Curved surface area (CSA) of a cylinder = 2πrh*

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*Workout Examples*

*Workout Examples*

*Example 1: Find the curved surface area of the given cylinder.*

*Solution:*

*Here,*

*Diameter of the cylinder (d) = 14cm*

*∴*

*Radius of the cylinder (r) = 14cm/2 = 7cm*

*Height of the cylinder (h) = 20cm*

*We know,*

**Curved surface area (CSA) = 2πrh**

*= 2 × 22/7 ×7 ×20*

*= 880cm*^{2}

^{}

*Thus, the curved surface area of cylinder is 880cm*^{2}.

*Example 2: The height of a cylinder is 15cm. The curved surface area is 660cm*^{2}. Find the radius of the base.

*Solution:*

*Here,*

*Height of the cylinder (h) = 15cm*

*Radius (r) = ?*

*Curved surface area (CSA) = 660cm*^{2}

*i.e. 2πrh = 660*

*or, 2 × 22/7 × r × 15 = 660*

*or, 660/7 × r = 660*

*or, r = 660 × 7/660*

*or, r = 7cm*

*Thus, the radius of the base is 7cm.*

*Example 3: The curved surface area of a right circular cylinder is 4400cm*^{2}and the circumference of its base is 110cm. Find the height of the cylinder.

*Solution:*

*Here,*

*Circumference of the cylinder = 110cm*

*i.e. 2πr = 110cm.*

*Curved surface area of the cylinder = 4400cm*^{2}

*i.e. 2πrh = 4400*

*or, 110h = 4400*

*or, h = 4400/110*

*or, h = 40cm*

*Thus, the height of the cylinder is 40cm.*

*You can comment your questions or problems regarding the CSA of cylinder here.*

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