Volume of Prisms

Solid geometry is concerned with three-dimensional shapes. In these lessons, we will learn

  • what is a prism?
  • how to find the volume of prisms.
  • how to solve word problems about prisms.

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Related Pages
Volume Formula
Volume Of Prism Worksheet
Volume Formulas Explained
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A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base.

The other faces are in the shape of parallelograms. They are called lateral faces.

The following diagrams show a triangular prism and a rectangular prism. triangular rectangular prism

A right prism is a prism that has its bases perpendicular to its lateral surfaces. If the bases are not perpendicular to its lateral bases then it is called an oblique prism.

When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.

cross section prism

What is a prism and distinguishes between a right prism and an oblique prism?

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

Volume of a Prism

The volume of a right prism is given by the formula:

Volume = Area of base × height = Ah

where A is the area of the base and h is the height or length of the prism.

Worksheet to calculate volume of prisms and pyramids.

Find the volume of the following right prism.

Volume = Ah
= 25 cm2 × 9 cm
= 225 cm3

Find the volume of the following right prism

First, we need to calculate the area of the triangular base.

We would need to use Pythagorean theorem to calculate the height of the triangle.

h2 + 32 = 52

Area of triangle =
= × 6 × 4
= 12 cm2

Volume of prism = Ah
= 12 cm2× 8 cm
= 96 cm3

How to find the volume of a rectangular and a triangular prism?
Step 1: Find the area of the base.
Step 2: Multiply the area of the base times the height.

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

Word problems about volume of prisms

The following video shows how to solve a word problem involving the volume of prisms.

Find the volume and capacity of a swimming pool which is made up of a rectangular and trapezoidal prism.

Use the given net to determine the surface area and volume of a triangular prism

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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