Cone : When we increase the base of square pyramid that base becomes circular and the figure changes to cone .

In real life we use this shape in funnel, joker’s cap etc.

Its base is circular and has a curved surface.

l^{2} = r^{2} + h^{2}Curved surface area = CSA = π r l Total surface area = TSA = π r ( r + l ) |

1) The diameter of a cone is 16 cm and its height is 6 cm. Find the surface area of cone.

l

l

⇒ = 64 + 36

⇒ = 100

l

∴ l = 10 cm

TSA(surface area of cone) = π r ( r + l )

⇒ = 3.14 x 8 ( 8 + 10)

⇒ = 3.14 x 8 x 18

∴ TSA = 452.16 cm

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2) A corn cob somewhat like a cone, has the radius of the broadest end as 2.1 cm and length as 20 cm. If each 1 cm

Total number of grains = CSA of corn cob x Number of grains on 1 cm

r = 2.1 cm and h = 20 cm

l = √( r

l = √( 2.1

⇒ = √( 4.41 + 400)

⇒ = √(404.41)

∴ l = 20.11 cm

CSA = π r l

⇒ = 3.14 x 2.1 x 20.11

∴ CSA of corn cob = 132.73 cm

Hence, the total number of grains on the corn cob = 132.73 x 4 = 530.92

So, there would be approximately 531 grains on the corn cob.

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3) A tent is of the shape of a right circular cylinder up to height 3 m and then becomes the right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of $2 per sq. m., if the radius of the base is 14 m.

r = 14 m and h = 3 m

CSA of cylinder = 2 x π x r x h

⇒ = 2 x 3.14 x 14 x 3

∴ CSA of cylinder = 263.76 m

For cone :

r = 14 cm and h = 13.5 – 3 = 10.5 m

l = √( r

l = √( 14

⇒ = √( 196 + 110.25 )

⇒ = √(306.25)

∴ l = 17.5 cm

CSA = π r l

⇒ = 3.14 x 14 x 17.5

∴ CSA of cone = 769.3 m

∴ Total area which is painted = CSA of cylinder + CSA of cone

⇒ = 263.76 + 769.3 = 1033.06 m

Hence, the cost of painting = 1033.06 x 2 = $2066.12 = $ 2066.

• 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 Cone to Mensuration>