Volume of Cone

Volume of Cone:
In general terms when we speak about a cone the first thing that comes to our mind is an ice-cream cone as depicted in the picture on the right hand side.

But to be more specific the meaning of a cone is given below "A cone is a three-dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.n geometry, there are two types of shapes." They are two dimensional and three dimensional.

Two dimensional shapes are rectangle, square, parallelogram, rhombus etc.

Three dimensional shapes are cone, sphere, pyramid, cube, prism.


Properties of cone:

There are two properties of cone . They are volume of cone, surface area of cone. By using the properties of cone, we can calculate volume and surface area.

A cone has radius (r) and height (h) , slant height (s).

Volume of cone V = 1/3 * π * radius2 * height where π = 3.14

Volume of cone V = 1/3 * Volume of cylinder

Surface area of cone SA = π*radius* [sqrt(radius^2+height^2)]

Total surface area of cone = Surface area + π*radius2.

In this blog we will also see some example problems related to Volume of a cone.By solving few problems we can understand how to calculate the surface of a cone.
Problem 1:

Find the volume of cone for the radius = 1 meter and height = 1 meter.

Solution:

Given radius = 1 meter

Height = 1 meter

Volume of cone = [1/3] * π * radius2 * height

= [1/3 ] * 3.14 * (1)2 * (1)

= [1/3] * 3.14 * 1 * 1

= [3.14/3]

= 1.05 m3.

Problem 2:

Find the Total Surface area of cone for the radius is 3 meter and height is 4 meter.

Solution:

Given: Radius = 3 m

Height = 4 m

Surface area of cone = π*radius* [sqrt(radius^2+height^2)]

= 3.14 * 3 * [sqrt(3^2+4^2)]

= 3.14 * 3 * [sqrt(9+16)]

= 3.14 * 3 * [sqrt(25)]

= 3.14 * 3 * 5

= 47.1 m2.

Total surface area of cone = Surface area + π*radius2.

= 47.1 + 3.14*32

= 47.1 + 3.14 * 9

= 47.1 + 28.26

= 75.36 m2.

Problem 3:

Find the height of a cone for the volume of cone is 100 cubic inches and radius of a cone is 5 inches.

Solution:

Given: Volume of cone V = 100 cubic inches

Radius of cone = 5 inches

Volume of cone = [1/3 ] * π * radius2 * height

100 = [ 1/3 ] * π * 52 * height

100 = [1/3] * 3.14 * 25 * height

100 = [1/3] * 3.14 * 25 * height

100 = [(3.14*25)/3] *height

100 = [78.5/3] *height

100 = 26.17 * height

Height = [100/26.17]

Height = 3.82 inches

Hope you like the above example of Surface area of cone.Please leave your comments, if you have any doubts.