Smart Math Formula, A cone is a three-dimensional geometric shape consisting of all line segments joining a single point to every point of a two-dimensional figure.

Slant height of Cone

[ l ] = Sqrt [r² + h²]

Volume of Cone = [1/3] πr²h

Curved Surface Area [ CSA ] of Cone = πrl

Total Surface Area [ TSA ] of Cone = πr [ l + r ]

Note :

*r = radius, l = slant height, h = height*### Example

Question : Find the volume, curved surface and total surface area of a cone with the given radius 3 and height 4.Answer : Find the slant height.

Slant height [ l ] = Sqrt [r² + h²] = Sqrt [3² + 4²]= Sqrt [9 + 16]

=Sqrt [25] = 5.

Answer : Find the volume.

Volume = [1/3]πr²h = [1/3] x 3.14 x 3² x 4 = 0.33 x 113.04 = 37.68.

Answer : Find the curved surface area [ CSA ].

CSA = πrl = 3.14 x 3 x 5 = 47.1.

Answer : Find the total surface area [ TSA ].

TSA = πr [l + r] = 3.14 x 3[5 + 3] = 3.14 x 3(8) = 3.14 x 24 = 75.36.

That is example will clearly illustrates how to calculate the Volume, Curved Surface and Total Surface Area of a Smart Math Formula Cone.