Question

In the right hexagonal pyramid below. The hexagonal base is regular and has sides that are 8 units long. The altitude of the pyramid is 18 units. Determine the volume of the pyramid to the nearest cubic unit.

Answer 1

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:

$V = \dfrac{1}{3} \times B \times h$

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.

$\text{Area of hexagon, B }= 6 \times \dfrac{\sqrt{3}}{4}a^{2}$

Here, a = 8 units

$\Rightarrow B = 6 \times \dfrac{\sqrt{3}}{4}\times 8^{2}\\\Rightarrow B = 166.27\text{ square units}$

Putting values of B and h in Formula of volume:

$\Rightarrow V = \dfrac{1}{3} \times 166.27 \times 18\\\Rightarrow V = \dfrac{2992.89}{3} = 997.62\text{ cubic units}$

Hence, the volume is 997.62 cubic units.