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

The volume is 997.62 cubic units..

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 = (1)/(3) * B * 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 * (√(3))/(4)a^(2)`

Here, a = 8 units

`\Rightarrow B = 6 * (√(3))/(4)* 8^(2)\\\Rightarrow B = 166.27\text{ square units}`

Putting values of B and h in Formula of volume:

`\Rightarrow V = (1)/(3) * 166.27 * 18\\\Rightarrow V = (2992.89)/(3) = 997.62\text{ cubic units}`

Hence, the volume is 997.62 cubic units.