Cone Formula and Cone Problems

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 (πr2). 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+ h2)

= √(6+ 32)

= √(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+ h2)

Radius = diameter /2

= 20/2

= 10 cm

Therefore,

Slant height (l)  = √(r+ h2)

= √(10+ 252)

= √(100 + 625)

= √(725)

= 26.92cm

Therefore the slant height of cone is 26.92cm.

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