## Cone Formula :

A right circular cone’s surface area is equal to the sum of its lateral surface area (πrl) and circular base surface area (πr^{2}). The formula for the Surface Area of the cone is,

**Area = πr(l + r) square units**

##### Curved Surface Area of Cone,

A cone’s curved surface area is the area enclosed by the curved part of the cone. The curved surface area of a cone with radius ‘r’, height ‘h’, and slant height ‘l’ is as follows, The formula for the curved surface area of a Cone,

**Area = πrl square units**

## Sample Problems :

### Example 1:

Calculate the total surface area of the cone with a radius of 6 cm and height of 3 cm?

### Solution :

Given: radius = 6 cm and

height = 3 cm,

Total surface area of cone is,

Area = πr(l + r)

Since, slant height l = √(r^{2 }+ h^{2})

= √(6^{2 }+ 3^{2})

= √(36 + 9)

= √42

Therefore,

Surface Area of Cone ,

Area = πr(l + r)

A = π * 6(√42 + 6)

= π * 6(6.48+ 6)

= π * 6(12.48)

= 22/7 * 6(12.48)

= 235.337square cm

### Example 2:

Calculate the slant height if diameter is 20 cm and the height of the cone is 25 cm?

### Solution :

Given: Diameter = 20 cm and

height of cone (h) = 25 cm

To find the slant height (l) = ?

l = √(r^{2 }+ h^{2})

Radius = diameter /2

= 20/2

= 10 cm

Therefore,

Slant height (l) = √(r^{2 }+ h^{2})

= √(10^{2 }+ 25^{2})

= √(100 + 625)

= √(725)

= 26.92cm

Therefore the slant height of cone is 26.92cm.