 # Volume of Prisms

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More Geometry Lessons

Solid geometry is concerned with three-dimensional shapes. In this lesson, we will learn

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

### Prisms

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. 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.

Example: 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.

Example:

Find the volume of the following right prism. Solution:

Volume = Ah
= 25 cm2 × 9 cm
= 225 cm3

Example:

Find the volume of the following right prism Solution:

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.
Example:
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

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