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.
Radius : The radius of the circular base is called the radius of the 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 h Area of base = π r2 Total 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 h Area 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 cm2.Find the diameter of the base of the cylinder. Solution : h = 14 cm ; CSA = 88 cm2
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
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
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( R2- r2)
= 2 x 3.14 x 12.5 x 20 + 2 x 3.14 x 11.5 x 20 + 2 x 3.14 ( 12.52 - 11.52)
= 1570 + 1444.44 + 6.28 ( 156.25 – 132.25 )
= 3014.4 + 148.8
TSA = 3163.2 cm2 Surface Area :