# Surface Area of Cylinder

Here we will discuss surface area of cylinder.

Cylinder : A solid generated by the revolution of a rectangular about one of its sides is called a right circular cylinder.
If we take a number of circular sheets and stake them up vertically , we get right circular cylinder. Base : Each of the circular ends on which the cylinder rests is called base.

Axis : The line segment joining the centers of two circular bases is called the axis of the cylinder. The axis is always perpendicular to the bases of right circular cylinder.

Height : The length if the axis of the cylinder is called the height of the cylinder.

Lateral surface or curved surface area of cylinder : The surface between the two circular bases is called its Lateral surface. When we cut the cylinder vertically we get a lateral surface in rectangular shape.

Formulas needed for Surface Area of Cylinder :
 Lateral Surface Area (LSA or CSA) = 2π r hArea of base = π r2Total Surface Area = TSA = 2 π r ( r + h)

Surface Area of Hollow Cylinder : A solid bounded by two coaxial cylinders of the same height and different radii is called a Hollow cylinder.

 Lateral Surface Area (LSA or CSA) = 2π r h + 2 π R hArea of base = π ( R2- r2)Total Surface Area = TSA = 2 πR h + 2π rh + 2 π( R2- r2)

Some solved examples on surface area of cylinder

1) The curved surface area of a right circular cylinder of height 14 cm is 88 cm
2 .Find the diameter of the base of the cylinder.
Solution : h = 14 cm ; CSA = 88 cm 2
CSA = 2 π r h
88 = 2 x 3.14 x r x 14
88 = 87.92 r = 88 r
∴ r = 1 cm
Diameter = d = 2r
d = 2 x 1 = 2 cm
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2) The ratio between the CSA and TSA of a right circular cylinder is 1:2. Find he ratio between the height and radius of the cylinder.
Solution :
TSA = 2 π r ( r + h)
CSA = 2 π r h
∴ CSA / TSA = 2 π r h / 2 π r ( r + h)
⇒ ½ = h / ( r + h )
2h = r + h
h = r
⇒ h : r = 1 : 1
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3) An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, find the whole surface of the pipe.
solution :
D = 25 cm ⇒ R = 12.5 cm
r = R – thickness = 12.5 – 1 = 11.5 cm
h = 20 cm
TSA of the pipe = 2 πR h + 2π r h + 2 π( R
2 - r 2 )
= 2 x 3.14 x 12.5 x 20 + 2 x 3.14 x 11.5 x 20 + 2 x 3.14 ( 12.5
2 - 11.5 2 )
= 1570 + 1444.44 + 6.28 ( 156.25 – 132.25 )
= 3014.4 + 148.8
TSA = 3163.2 cm
2

Surface Area :

Surface Area of Cube
Surface Area of Rectangular Prism(Cuboid)
Surface Area of Cylinder
Surface Area of Cone
Surface Area of Sphere and Hemisphere
Surface Area of Prism
Surface Area of Pyramid

From Cylinder to Mensuration