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Concept Detail
Maths / Surface Area and Volume / Lateral Surface Area of Cone
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Lateral Surface Area of Cone

Lateral Surface Area of Cone: The curved surface area of a cone is also called the lateral surface area. Lateral surface area of cone =pi rl

where r = radius of the base of the cone and l = slant height of the cone and large l=sqrt{r^2+h^2}

Illustration: The circumference of the base of a 10m height conical tent is 44m. Calculate the length of canvas used in making the tent if width of canvas is 2m.

Solution: Given: Circumference of cone = 44 m and h =10m and breadth = 2 m

So, we have, large 2pi r = 44m ..............(i)

So, Using equation (i), we have

  large 2times frac{22}{7}times r=44

frac{44}{7}times r=44

r=44times frac{7}{44}

r=7;m

As we know Area of Canvas = Curved Surface Area of Cone

Area of Canvas = length x breadth = length x 2             ...................(ii)            [As breadth = 2 m]

large  therefore; l=sqrt{r^2+h^2}=sqrt{49+100}=sqrt{149}m  = 12.2 m

large Lateral ;surface;area=pi rl=frac{22}{7}times 7times sqrt{149}m^2=268.4m^2

Now, using equation (ii), we have

Area of Canvas = length x 2  

length =frac{area ;of; canvas}{2}

Length of canvas = large frac{268.4}{2}=134.2m

Illustration:  The radius and slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 sq cm, find its radius. (Use large pi =frac{22}{7})

Solution: Let r cm be the radius and l cm the slant height of the cone. Then,

r : l = 4 : 7

Let the common factor = x

large therefore r= 4x cm and large l= 7x cm         ........................(i)

Now, curved surface area = 792 sq cm

large pi rl =792

large frac{22}{7}times 4xtimes 7x=792

large x^{2}=frac{792}{88}

large x^{2}=9

large x=pm 3

But x = - 3  is not possible.

Hence, x = 3

Using x = 3 in equation (i), we have

large r= 4x=4(3)

large r=12 cm

Hence radius of the base of the cone is 12 cm.


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