### What is a Prism?

In this overview we’re walk to display you how to job-related out the volume of a prism. Before we obtain to working out the volume though, it’s essential to price a basic question: what actually is a prism?

Well, a prism is a three dimensional shape which has the very same two dimensional shape repeated along its length. Take a look in ~ the examples below. All of these shapes are prisms. Notification how they have the same two dimensional shape (a rectangle, triangle or trapezium in these examples) recurring throughout your length. We will call this 2 dimensional shape the cross-section.

### The Formula for the Volume of a Prism

You may see various formulas for working out the volume of different prisms, but they every follow this same rule:

Volume the a prism = Area the the Cross-Section x Length

The cross-section is the two dimensional shape repetitive throughout the prism’s length. You simply work the end the area the this cross-sectional form (using your expertise on area) and then multiply the area by the length (sometimes described as the depth). Examine out these examples below to assist build your understanding.

### Examples

Example 1 – Cuboid

Let’s start by working out the volume the this cuboid.

Example 1 – Cuboid

This is a kind of prism, with a rectangle repetitive throughout the shape’s length. Here’s just how we should technique the dearteassociazione.orgncern and dearteassociazione.orgllection out our working:

Volume of prism = Area of cross-section x Length

Volume of instance 1 = Area and also rectangle x Length

= base x height x Length

= 8 x 3 x 10

= 240cm3

Example 2 – triangular Prism

Work out the volume the this triangular prism.

You are watching: What is the cross section of a prism

Example 2 – triangular Prism

This form of prism has actually a triangle as the cross-section, therefore we’re walking to occupational out the area the the triangle (check out our area guide for assist here) and then multiply that by the length.

Volume that prism = Area the cross-section x length

Volume of example 2 = Area the triangle x depth

= (1/2 x basic x height) x length

= (1/2 x 6 x 4) x 9

= 12 x 9

= 108cm3

Example 3 – Trapezoidal Prism

Work the end the volume that this trapezoidal prism.

Example 3 – Trapezoidal Prism

Here we have a prism with a trapezium as the cross-section. We’re walking to usage the exact same formula for working out the volume of a prism. We’ll disdearteassociazione.orgver the area that the cross-section (which is a trapezium in this example) and also then main point by the size to job-related out the volume. Again, if you have to revise the area the a trapezium then you should check our revision overview on area together well.

Volume the prism = Area of cross-section x length

Volume of instance 3 = Area of trapezium x length

= 0.5 x (a + b) x h x length

= 0.5 x (7 + 9) x 5 x 8

= 40 x 8

= 320 cm3

That is quite much every little thing you need to know on this topic. Firstly, occupational out the area the the cross-section. Then just multiply by the length and also you have your answer. Check out some more good support ~ above this topic native BBC bitesize to help you practice.

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