Truncated pyramid volume calculator

From ancient times, people needed to measure the amount of various substances. Bulk substances and liquids could be measured by filling them with vessels of a certain capacity, determining their quantity by volume. The concept of volume in solid geometry is introduced similarly to the concept of area in plane geometry. In plane geometry, we determined the area like this: the area of ​​a polygon is the value of the part of the plane that the polygon occupies. To formulate the concept of volume similarly to this concept. The magnitude of the part of the space occupied by the geometric body is called the volume of this body. Volume is measured in "cubic" units.

A truncated pyramid is a polyhedron whose vertices are the vertices of the base and the vertices of its section with a plane parallel to the base. Properties of a truncated pyramid: Lateral faces of a truncated pyramid - a trapezoid. The lateral ribs of a regular truncated pyramid are equal and equally inclined to the base of the pyramid.

A truncated pyramid is a pyramid with its top cut off by a plane parallel to its base. To find the volume of a truncated pyramid, you can use the following formula:

V = \dfrac{1}{3}h\left( S_1 + \sqrt{S_1S_2} + S_2 \right)

where V is the volume of the truncated pyramid, h is the height of the truncated pyramid, and S₁ and S₂ are the areas of the top and bottom sides of the truncated pyramid.

Our truncated pyramid volume calculator makes it easy to find the volume of your truncated pyramid. Simply enter the height of the truncated pyramid, the area of the top and bottom bases, and our calculator will automatically give you the volume.

Here's how to use the calculator:

1. Enter the area of the bottom base of the truncated pyramid in the first box.
2. Enter the area of the top base of the truncated pyramid in the second box.
3. Enter the height of the truncated pyramid in the third box.
4. The calculator will automatically calculate the volume of your truncated pyramid.

Truncated Pyramid Volume Examples

Here are some examples of finding the volume of a truncated pyramid using the formula:

Example 1

Find the volume of a truncated pyramid with a height of 5 units, a top area of 7 units, and a bottom area of 9 units.

V = \dfrac{1}{3}5\left( 7 + \sqrt{7*9} + 9 \right)

V = \dfrac{1}{3}5*7.93

V = 39.9 \text{cubic units}

Example 2

Find the volume of a truncated pyramid with a height of 8 units, a top area of 4 units, and a bottom area of 10 units.

V = \dfrac{1}{3}8\left( 4 + \sqrt{4*10} + 10 \right)

V = \dfrac{1}{3}8*6.32

V = 54.2 \text{cubic units}

Conclusion

Calculating the volume of a truncated pyramid is an important skill in geometry. Our truncated pyramid volume calculator and formula make it easy to find the volume of your truncated pyramid. Try it out for yourself and see how easy it can be!