Area of a Cone Shape

Introduction :
                    Cone is the one type of three dimensional shapes. It has one base and one vertex. The base of the cone is circle in shape. It surface is tappers smoothly towards the top. The distance between center of the base and any point on the boundary of base is called radius. In this article we shall see how to calculate the volume and surface area of the cone.


Area of a Cone Shape – Formula:

Formula for volume of the cone (v) =`1/3` p r^2 h cubic units

                                                    v - Volume of cone

                                                    r – Radius

                                                    h – Height 

Surface area of cone (A) = lateral surface area of cone + area of base 

                                              = p r s    + p r^2 square unit 

                                                s – Slant height

Area of a Cone Shape – Example Problems:

1. The cone has the radius = 7 cm, height = 14 and slant height = 15.6 cm. Find the volume of the cone.

Solution:

 Given:

                        Radius (r) = 7 cm

                        Height (h) = 14 cm

                      Slant height (s) = 15.6 cm

Formula:

Total surface area:

Total Surface area of cone (A) = lateral surface area of cone + area of base

Lateral surface area (L.S.A) = p r s    square unit.

Substitute the r and s value in formula and simplify,

                                                           = p x 7 x 15.6

                                                            = 3.14 x 7 x 15.6

                                                            = 342.88 cm3

       Lateral surface area (L.S.A) = 204.1 cm^2

                          Area of base = p r^2 square unit

                                                    = 3.14 x 72

                           Area of base = 153.86 cm^2

Total Surface area of cone (A) = lateral surface area of cone + area of base

                                                    = 204.1 +153.86

                                                    = 357.96 cm^2

   2. The cone has the radius = 8 cm, height = 15 and slant height = 17 cm. Find the volume of the cone.

Solution:

 Given:

                        Radius (r) = 8 cm

                        Height (h) = 15 cm

                     Slant height (s) = 17 cm

Formula:

Total surface area:

Total Surface area of cone (A) = lateral surface area of cone + area of base

Lateral surface area (L.S.A) = p r s    square unit.

Substitute the r and s value in formula and simplify,

                                                     = p x 8 x 17

                                                     = 3.14 x 8 x 17

                                                     = 427.04

Lateral surface area (L.S.A) = 427.04 cm^2

                          Area of base = p r^2 square units

                                                  = 3.14 x 8^2

                         Area of base = 200.96 cm^2

Total Surface area of cone (A) = lateral surface area of cone + area of base 

                                                         = 427.04 + 200.96

                                                         = 628 cm^2
Understanding how to solve proportions with variables is always challenging for me but thanks to all math help websites to help me out.