Volume of a Hexagonal Pyramid Calculator

Created by Mehjabin Abdurrazaque
Reviewed by Kenneth Alambra
Last updated: Mar 01, 2022

With the volume of a hexagonal pyramid calculator, you can find the volume of a hexagon-based pyramid using:

  • the height (altitude) and base edge;
  • the height and slant height;
  • the slant height and base perimeter;
  • the slant height and base edge; etc.

Excited? Let's quickly learn how to find the volume of a hexagon-based pyramid and try the calculator!

What is a hexagonal pyramid?

A hexagonal pyramid is a three-dimensional object with a hexagon-shaped (6 sides) base and six triangular faces originating from each side to a common vertex.

  • The distance between the center of the hexagonal base and the common vertex is the altitude or height (h) of the pyramid.
  • The length of the base's side is the base edge or base length (a) of the pyramid.
  • The distance between the midpoint of the base edge and the vertex is the slant height (l) of the pyramid.
  • The distance between the midpoint of the base edge and the center of the hexagonal base is the pyramid's apothem (ap).

How do I calculate the volume of a hexagon-based pyramid?

We calculate the volume of a regular hexagonal pyramid using the formula:

  • V = (√3/2) a2 h

where

  • V is the volume of the hexagon-based pyramid;
  • a is the length of the base edge; and
  • h is the height of the pyramid.

How do I use the volume of a hexagonal pyramid calculator?

❓ What is the volume of a regular hexagonal pyramid that has a base perimeter of 12 cm and an altitude of 15 cm?

We need to find the volume using the base perimeter and altitude of the pyramid. To do this:

  1. Check if the variables on the volume of a hexagonal pyramid calculator have our desired units. If they don't show our desired units, select the unit from the drop-down list in their row. The default unit is centimeter (cm) and cubic centimeter (cm3). In our example problem, we know the base perimeter and the altitude in centimeters (cm), so we don't have to change their default units in the calculator.
  2. Enter 12 in the input box for Base perimeter (P).
  3. Enter 15 in the input box for Height (h).

That's all you have to do! The volume of a hexagonal pyramid calculator will give you the following results:

  • Base edge (a) - 2 cm;
  • Slant height (l) - 15.1 cm;
  • Apothem (ap) - 1.732 cm; and
  • Volume (V) - 51.96 cm3.

FAQ

What is the formula for a hexagonal pyramid's volume using apothem and height?

If the base edge is unknown, we can calculate the volume of a regular hexagonal pyramid from apothem (ap) and height (h) using the formula V = (2/√3) × ap2 × h or V = 1.1547 × ap2 × h.

How do I find the volume of a hexagonal pyramid using apothem and base-edge?

If we know the apothem, base edge, and height of a hexagonal pyramid, we use the following formula to calculate its volume:

  • V = ap × a × h

where,

  • ap is the apothem of the hexagonal pyramid;
  • a is the length of the base edge; and
  • h is the height or altitude of the pyramid.

How do I estimate the volume of any pyramid?

For a pyramid with a regular base,

  • V = (n/12) × h × a2 × cot(π/n)

where

  • V is the volume of the pyramid;
  • n is the number of sides of its base;
  • h is the height of the pyramid; and
  • a is the length of the base edge.

Find the height of a hexagonal pyramid of volume 810 and base edge 9 units.

The height of the hexagonal pyramid is 11.55 units. The volume (V) of a hexagonal pyramid of base edge (a) and height (h) is:

  • V = (√3/2) a2 h

Thus, the height is

  • h = 2V/(√3 a2)

Volume calculators for various three-dimensional objects

Would you like to see more 3D volume calculators? Please write to us. You will also love our surface area calculator 🙂

Mehjabin Abdurrazaque
Surface area of a pyramid
Height (h)
in
Base edge (a)
in
Apothem (aₚ)
in
Slant height (l)
in
Base perimeter (P)
in
Base area (BA)
in²
Volume (V)
cu in
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