Answer:
The volume is 997.62 cubic units..
Step-by-step explanation:
We are given the following details:
The pyramid has a regular hexagonal base i.e. each side of hexagon is equal.
Side of hexagonal base, a = 8 units
Altitude of pyramid, h = 18 units
We have to find the volume of pyramid.
Formula:
[tex]V = \dfrac{1}{3} \times B \times h[/tex]
Where, B is the area of base of pyramid.
h is the height/altitude of pyramid
To calculate B:
Here, base is a hexagon with side 8 units.
[tex]\text{Area of hexagon, B }= 6 \times \dfrac{\sqrt{3}}{4}a^{2}[/tex]
Here, a = 8 units
[tex]\Rightarrow B = 6 \times \dfrac{\sqrt{3}}{4}\times 8^{2}\\\Rightarrow B = 166.27\text{ square units}[/tex]
Putting values of B and h in Formula of volume:
[tex]\Rightarrow V = \dfrac{1}{3} \times 166.27 \times 18\\\Rightarrow V = \dfrac{2992.89}{3} = 997.62\text{ cubic units}[/tex]
Hence, the volume is 997.62 cubic units.
