Curved surface area of cylinder is the measurement of outer area, where the extension of top and bottom portion wont be included.
If a rectangle revolves about one side and completes one full rotation, the solid thus formed is called a right circular cylinder. The above picture shows that how rectangle forms a right circular cylinder. In other words curved surface area is simply said as CSA
CSA of cylinder = 2 π r h
"r" and "h" stands for radius and height of cylinder.
A hollow cylinder is a three dimensional solid bounded by two parallel cylindrical surfaces and by two parallel circular bases cut out from two parallel planes by these two cylindrical surfaces.
CSA of hollow cylinder = 2πh(R+r)
R = external radius, r = internal radius and h = height
Example 1 :
A solid right circular cylinder has radius of 14 cm and height of 8 cm. Find its CSA.
Solution :
Radius of the cylinder (r) = 14 cm
Height of the cylinder (h) = 8 cm
Curved surface area of cylinder = 2Πrh
= 2⋅ (22/7) ⋅ 14 ⋅ 8
= 704 sq.cm
Curved surface area of cylinder = 704 sq.cm
So, curved surface area of cylinder is 704 sq.cm
Example 2 :
Curved surface area and circumference at the base of a solid right circular cylinder are 4400 sq.cm and 110 cm respectively. Find its height and diameter.
Solution :
CSA of cylinder = 4400 sq.cm
Circumference of the base = 110 cm
2Πr = 110 ==> 2 ⋅ (22/7) ⋅ r = 110
r = 110 ⋅ (1/2) ⋅ (7/22)
r = 17.5 cm
diameter = 2r = 2(17.5)
diameter = 35 cm
2 Π r h = 4400
110 ⋅ h = 4400
h = 4400/110
h = 40 cm
Height = 40 cm
Diameter of the cylinder = 35 cm
So, height and diameter of cylinder is 40 cm and 35 cm respectively.
Example 3 :
A mansion has 12 right cylindrical pillars each having radius 50 cm and height 3.5 m. Find the cost to paint the curved surface of pillars at $ 20 per square meter.
Solution :
The pillars of the mansion are in the shape of cylinder
Radius = 50 cm ==> 0.5 m
Height = 3.5 m
CSA of one pillar = 2 ⋅ (22/7) ⋅ 0.5 ⋅ 3.5
= 2 ⋅ 22 ⋅ 0.5 ⋅ 0.5 ==> 11 m^{2}
CSA of 12 pillars = 12 ⋅ 11
= 132 m^{2}
Cost to paint per m^{2} = $ 20
Total cost = 20 ⋅ 132
= $ 2640
Hence, total cost of painting 12 pillars is $ 2640
Example 4 :
The total surface area of a solid right circular cylinder are 231 cm². Its curved surface area is two thirds of the total surface area. Find the curved surface area if cylinder.
Solution :
Curved surface area = (2/3) ⋅ Total surface area
2 Π r h = (2/3) ⋅ 231
2 Π r h = 2 ⋅ 77
2 Π r h = 154
Hence, curved surface area of cylinder is 154 cm^{2}
Example 5 :
The total surface area of a solid right circular cylinder is 1540 cm². If the height is four times the radius of the base, then find the CSA of cylinder.
Solution :
Total surface area of cylinder = 1540 cm²
CSA of cylinder + top area + bottom area = 1540 cm²
2 Π r (h + r) = 1540
h = 4 ⋅ radius of the base
h = 4 r
2 Π r (4r+r) = 1540
2 Π r (5r) = 1540
2 ⋅ (22/7) ⋅ 5 r^{2} = 1540
= 1540 ⋅ (1/2) ⋅ (7/22) ⋅ (1/5)
= (1540 ⋅ 7)/(2 ⋅ 22 ⋅ 5)
= (1540 ⋅ 7 )/(2 ⋅ 22 ⋅ 5)
r^{2} = 49
r = √(7⋅7)
r = 7 cm
Curved surface area of cylinder :
= 1540 - 2 ⋅ (22/7) ⋅ 7 ⋅ 7
= 1540 - 308
= 1232 cm^{2}
Hence, CSA of cylinder = 1232 cm^{2}.
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