Right Hexagonal Prism

Introduction to right hexagonal prism
      A right prism is a prism within which the apex and base polygons lie down on the top of every other.Therefore to the vertical polygons joining their faces are not only parallelograms, but rectangles. A prism to be not a right prism is recognized as an oblique prism. If, also, the higher and inferior bases are rectangles, after that the prism is recognized as a cuboid.

Right Hexagonal Prism

A hexagonal prism is a prism collected of 6 rectangular faces and 2 hexagonal bases. It is also identified as octahedron.

The usual right hexagonal prism of edge length a contain surface area also volume.

`S=3(2+sqrt(3))a^2`

`V=3/2sqrt(3)a^3`

The usual right hexagonal prism is a gap-filling polyhedron.

Examples for Right Hexagonal Prism

Example 1

Find the volume of a right hexagonal prism to contain base edges of 11 meters and a height of 30 meters?

Solution:

Given

height = 30 m

base edge = 11 m

The six sides of the bottom hexagon are all of length 11m.

Let us consider the mean to the hexagon is regular.

Area of a regular hexagon of side a is `A=(3 sqrt(3))/2 a^2`

Therefore the base area of the prism is `A=(3 sqrt(3))/2xx 11^2`

                    A = 112 x 2.6                     {since `(3 sqrt(3))/2` =2.6}

                      = 121 x 2.6

Area of the hexagon  = 314.6 m2

Volume of a right prism is V = Ah

Wherever A - base area

h - Height.

Therefore the volume of prism is V = 314.6 x 30

Therefore the volume of prism is V=9438 m2

Example 2

Find the volume of a right hexagonal prism to contain base edges of 16 meters and a height of 40 meters?

Solution:

Given

height = 40 m

base edge = 16 m

The six sides of the bottom hexagon are all of length 16 m.

Let us consider the mean to the hexagon is regular.

Area of a regular hexagon of side a is `A=(3 sqrt(3))/2 a^2`

Therefore the base area of the prism is `A=(3 sqrt(3))/2xx 16^2`

                    A = 162 x 2.6                     {since `(3 sqrt(3))/2` =2.6}

                      = 256 x 2.6

Area of the hexagon  = 665.6 m2

Volume of a right prism is V = Ah

Wherever A - base area

 h - Height.

Therefore the volume of prism is V = 665.6 x 40

Therefore the volume of prism is V=26624 m2