Introduction to hexagonal prism:
A hexagonal prism is defined as the prism which is composed of two hexagonal bases and six rectangular sides. Generally it is look like an octahedron.
The regular of the right hexagonal prism's edge length ‘a’ has surface area and volume
The surface area for the hexagonal prism is given by,
S = 3(2 + `sqrt(3)` )a2 square units
The volume for the hexagonal prism is given by,
V = `(3)/(2)` `sqrt(3)`a3 cubic units
More about the Volume of Hexagonal Prism
Due to the structure of the hexagonal prism, the measures of the prism are varying by the methods. Another method is that it would be considering the side of the apothem as 'a', side as 's', height as 'h' in the hexagonal prism given below.
Surface area of the regular hexagonal prism = 6 × apothem (a) × side length (s) + 6 × side length (s) × height (h).
It is represented in square units.
Volume of the hexagonal prism = 3 × apothem (a) × side length (s) × height (h).
It is represented in cubic units.
Examples for the Volume of Hexagonal Prism
Consider the hexagonal prism with the same length 5 cm .calculate the surface area and volume of the hexagonal prism.
Solution:
The surface area for the hexagonal prism is given by,
S = 3(2 + `sqrt(3)` )a2 square units
S=3 (2 + `sqrt(3)` ) 52
S=279.90 cm2 is the required surface area of the hexagonal prism
The volume for the hexagonal prism is given by,
V = `(3)/(2)` `sqrt(3)`a3 cubic units
V = `(3)/(2)` `sqrt(3)`53
V = 64.951 cm3 is the required volume of the hexagonal prism
Another method:
2. Consider the hexagonal prism for to calculate the surface area and volume of the hexagonal prism by considering the side of the apothem as '5', side as '4', height as '3' and all units are in centimetres.
Solution:
Surface area of the regular hexagonal prism = 6 × apothem (a) × side length (s) + 6 × side length (s) × height (h) square units.
Surface area of the regular hexagonal prism = 6 × 5 x 4 x 3
=360 cm2 is the required surface area of the hexagonal prism
Volume of the hexagonal prism = 3 × apothem (a) × side length (s) × height (h) cubic units.
Volume of the hexagonal prism = 3 × 5 x 4 x 3
=180 cm3 is the required volume of the hexagonal prism
