Volume of Hexagonal Cylinder

The volume of a hexagonal cylinder is the number of unit cubes that can be fit into it. The unit of volume is "cubic units". A hexagonal cylinder is a geometric three-dimensional object that has two parallel hexagonal bases and six side faces. A hexagon is a two-dimensional object, and its equivalent in a three-dimensional plane becomes a hexagonal cylinder. The hexagonal cylinder is very common in our daily life and can be seen in many places such as gym weights, nuts, pencils, buildings, vases, etc.
There are two types of hexagonal cylinders.

• A regular hexagonal cylinder - A regular hexagonal cylinder has regular hexagons as bases.
• An irregular hexagonal cylinder - An irregular hexagonal cylinder has irregular hexagons as bases.

The volume of a hexagonal cylinder is the total space that is enclosed in a three-dimensional plane. A cylinder is made up by extending the hexagonal face upwards up to a distance which is called the height of a hexagonal cylinder. There are two parallel bases and six sides known as faces in a hexagonal cylinder. Also, this cylinder has 18 edges, 8 faces, and 12 vertices. It has 6 rectangle faces and 2 hexagonal faces out of the 8 faces while the opposite faces are the same.

Let us consider a hexagonal cylinder of base edge length 's', height 'h, and the volume of a hexagonal cylinder is 'V'. Since the bases of the hexagonal cylinder is in a hexagonal shape whose area is (3√3/2)s² and its height is considered as 'h'. We know that the volume of any cylinder is its base area multiplied by its height. So the volume of the hexagonal cylinder becomes (3√3/2)s² × h. The unit of volume is "cubic units". For example, it can be expressed as m³, cm³, km³, etc depending upon the given unit of length. Let us see how to find the formula of the volume of a hexagonal cylinder.

We know that base of a hexagonal cylinder is a hexagonal plane and hence its area is, (3√3/2)s². The height of the cylinder is 'h'. So its volume is

V = base area × height = (3√3/2)s² × h

By the above formula, we can say that the volume of a hexagonal cylinder is (3√3/2) times of product square of its base edge length and its height.

As we learned in the previous section, the volume of any cylinder is its base area multiplied by its height which is, V = (3√3/2)s² × h. Thus, we follow the steps shown below to find the volume of a hexagonal cylinder.

• Step 1: Identify the base edge length and name it to be s or a; Identify its height and name it to be h.
• Step 2: Find the volume using the formula V = (3√3/2)s² × h.
• Step 3: Represent the final answer in cubic units.

Example

Find the volume of a hexagonal cylinder of base edge length 3 units and height 7 units.

Solution

The base edge length, s = 3 units.

Its height, h = 7 units.

Its volume is,

V = (3√3/2)s² × h

V = (3√3/2)3² × 7

V = 163.67 cubic units.

Therefore, the volume of the given hexagonal cylinder is 163.67 cubic units.

What Is Meant By the Volume of the Hexagonal Cylinder?

The volume of a hexagonal cylinder is the total space occupied by the 3-D shape. The volume of the hexagonal cylinder is V = (3√3/2)s² × h, where 's' is base edge length and 'h' is the height of a cylinder.

What Is the Formula for Volume of a Hexagonal Cylinder?

The volume of the hexagonal cylinder can be calculated using the base area and height. When the base area is multiplied by the height of a 3-d object, thus the formula of volume of any object is obtained.

What Is Unit Used to Express Volume of Hexagonal Cylinder?

In measurements, the volume of a hexagonal cylinder is expressed in cubic units. The common units used are in³, m³, cm³, ft³, yd³, etc.

How Will the Volume of a Hexagonal Cylinder Change When the Base Length Is Doubled?

The volume of a hexagonal cylinder is proportional to the square of the base length. Therefore, the volume gets quadrupled when the radius is doubled.

What Is the Apothem of a Hexagonal Cylinder?

The apothem of a hexagonal cylinder is the apothem length of the hexagon-shaped base. A regular hexagon has six equal sides. An apothem is a line segment that is taken from the center of a polygon to the middle point of any one side of a hexagon.
The formula for apothem is,
Apothem = s/[2tan(180/n)]
where,

• 's' is the base edge length.
• 'n' is the number of sides of a polygon.

What Is the Surface Area of a Hexagonal Base of a Hexagonal Cylinder?

The surface area of a hexagonal cylinder is the total area or region occupied by all the faces and base of the hexagonal cylinder. The formula for the surface area of a hexagon is given as, SA = (3√3/2)s², where SA is the surface area and s is the side length of a hexagon.