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Volume in Geometry (examples, solutions)

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A series of free, online High School Geometry videos, lessons and solutions.
Videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

  • the properties of 3-dimensional solids
  • how to find the volume of prisms
  • how to find the volume of cylinders
  • how to find the volume of cones

3-D Solid Properties

When talking and learning about 3-dimensional solids, there are a few important terms and solid properties that we need to know. One of the first things we need to know is how to label the parts of a prism such as vertices, edges, bases and lateral faces. It is also important to be able to distinguish between an oblique and a right prism.

How to label the parts of a prism, how to distinguish between an oblique and a right prism.

Volume of Prisms

We can calculate the volume of any prism simply by knowing the height of the prism and the area of one of its bases. When calculating prism volume, this volume formula can be applied to both right and oblique prisms with bases of any shape, such as triangles, quadrilaterals, or other polygons. A prism volume is a measurement of the space occupied by such solid.

How to find the volume of any prism, right or oblique using a general formula.

Volume of Prisms

Volume of Cylinder

The prism volume formula of height times the area of one of the bases can also be applied when calculating the volume of cylinders. To find the volume of a cylinder we simply multiply the height of the cylinder times the area of a circle of one of the bases. By simply knowing this formula, we are able to find missing heights and base measurements in cylinder volume problems.

How to calculate the volume of any cylinder.

The video provides two examples of finding the volume of a cylinder.

Volume of Cone

The formula for the volume of cylinders can also be applied to the volume of cones, which occupy only one third of the space of a corresponding cylinder with the same base and height. To find volume of cone dimensions and measurements, we simply use the formula for the area of a circle for one of the bases and then multiply by one third of the height of the cone. This formula is very similar to volume of cylinder and prism volume formulas.

How to Find the Volume of a Cone

This video provides a specific example of how to find the volume of a cone given the radius and the slant height.

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