Mathematics
Grade9
Easy
Question
Basaltic columns are geological formations that result from rapidly cooling lava. The Giant’s Causeway in Ireland, pictured here, contains many hexagonal columns. Suppose that one of the columns is in the shape of a regular hexagon with a radius of 8 inches.
What is the apothem of the column?
- 6.92 inches
- 8.56 inches
- 2.34 inches
- 9.43 inches
Hint:
A perpendicular line segment joining the centre and one of the sides of the regular polygon is called apothem of the polygon. Here, we have to find the apothem of the given polygon.
The correct answer is: 6.92 inches
In the question it is given that there is a regular hexagon with a radius of 8 inches.
Here, we have to find the apothem of the given regular hexagon.
Firstly, we have to find the central angle of the given regular hexagon.
Central angle = 
= 60
Since, apothem bisects the central angle.
So, cos 30 = 
= 
(where, a= apothem)
a = 6.92 inches
So, the apothem of the given regular hexagon is 6.92 inches.
Therefore, the correct option is a, i.e., 6.92 inches.
Angle is a figure which is formed when two rays meet at a common point. Angles can be of many types one of them is central angles. Central angle is formed when two radii of a circle meet at the centre the circle. Central angle of a regular polygon can be determined by using the formula 
.
