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

where r = radius of the base of the cone and l = slant height of the cone and

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, = 44m ..............(i)

So, Using equation (i), we have

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]

  = 12.2 m

Now, using equation (ii), we have

Area of Canvas = length x 2  

length

Length of canvas =

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 )

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

cm and cm         ........................(i)

Now, curved surface area = 792 sq cm

But x = - 3  is not possible.

Hence, x = 3

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

cm

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