OwlCalculator
OwlCalculator
  • Conversions
  • Health
  • finance Finance Calculator
  • Statistics
  • Combinatorics
  • Percentage Calculators
  • Arithmetic
  • math-curve Algebra
  • Geometry
  • Physics
  • Chemistry

Truncated pyramid volume calculator

Volume

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.

Truncated Pyramid

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.

Truncated pyramid volume

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!

Follow Us

Tags

truncated pyramid volume truncated pyramid volume calculator truncated pyramid volume formula
  • Area
  • Volume
  • Perimeter
  • Side
  • Height
  • Diagonal
  • Radius
  • Median
  • Bisector
  • Angle
  • Theorems
  • Triangle area
  • Square Area
  • Rectangle Area
  • Circle Area
  • Rhombus Area
  • Parallelogram Area
  • Trapezoid Area Calculator
  • Ellipse Area
  • Annulus Area
  • Quadrilateral Area
  • Annulus Sector Area
  • Circle Sector Area
  • Circle Segment Area
  • Sphere area
  • Cube Area
  • Cylinder area
  • Pyramid area
  • Parallelepiped area
  • Cone area
  • Truncated cone area
  • Tetrahedron area
  • Regular polygon area
  • Sphere volume
  • Cube volume
  • Cylinder volume
  • Pyramid volume
  • Parallelepiped volume
  • Cone volume
  • Truncated cone volume
  • Tetrahedron volume
  • Prism volume
  • Octahedron volume
  • Truncated pyramid volume
  • Ellipsoid volume
  • Capsule volume
  • Hemisphere volume
  • Spherical segment volume
  • Triangle perimeter
  • Square perimeter
  • Rectangle perimeter
  • Circle perimeter
  • Rhombus perimeter
  • Parallelogram perimeter
  • Trapezoid perimeter
  • Ellipse perimeter
  • Annulus perimeter
  • Quadrilateral perimeter
  • Circle sector perimeter
  • Regular polygon perimeter
  • Triangle side calculator
  • Square side calculator
  • Rectangle side calculator
  • Rhombus side calculator
  • Parallelogram side calculator
  • Trapezoid side calculator
  • Cube side calculator
  • Parallelepiped side calculator
  • Pyramid side calculator
  • Tetrahedron side calculator
  • Triangle height calculator
  • Trapezoid height calculator
  • Parallelogram/Rhombus height calculator
  • Pyramid height calculator
  • Prism height calculator
  • Cylinder height calculator
  • Cone height calculator
  • Square diagonal calculator
  • Rectangle diagonal calculator
  • Rhombus diagonal calculator
  • Parallelogram diagonal calculator
  • Trapezoid diagonal calculator
  • Cube diagonal calculator
  • Parallelepiped diagonal calculator
  • Cylinder diagonal calculator
  • Circle radius calculator
  • Cylinder radius calculator
  • Sphere radius calculator
  • Triangle median calculator
  • Triangle bisector calculator
  • Parallelogram bisector calculator
  • Trapezoid bisector calculator
  • Triangle angles
  • Rhombus angles
  • Sine of angle
  • Cosine of angle
  • Tangent of angle
  • Cotangent of angle
  • Pythagorean theorem
  • Sinus theorem
  • Cosine theorem
  • Tangens theorem
  • Cotangent theorem
  • Tangent-Secant theorem

OwlCalculator

2019-2025

Information F.A.Q About Us Terms of Service Privacy Policy Contact Us
Follow Us

© Copyright by iForce Systems LLC