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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.

Formulas needed for Surface Area of Cylinder :

Lateral Surface Area (LSA or CSA) = 2π r h Area of base = π r ^{2}Total Surface Area = TSA = 2 π r ( r + h) |

Lateral Surface Area (LSA or CSA) = 2π r h + 2 π R h Area of base = π ( R ^{2}- r^{2})Total Surface Area = TSA = 2 πR h + 2π rh + 2 π( R ^{2}- r^{2}) |

1) The curved surface area of a right circular cylinder of height 14 cm is 88 cm

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.

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.

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 x 3.14 x 12.5 x 20 + 2 x 3.14 x 11.5 x 20 + 2 x 3.14 ( 12.5

= 1570 + 1444.44 + 6.28 ( 156.25 – 132.25 )

= 3014.4 + 148.8

TSA = 3163.2 cm

• 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

8th grade math

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