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All courses Math Foundations · MF.GM.6 53 of 60
Find and interpret volume of prisms and cylinders using correct units.

Multiply the three rectangular-prism dimensions

Problem
A rectangular prism is \(3~\text{units}\) long, \(4~\text{units}\) wide, and \(6~\text{units}\) high. What is its volume?
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Hint

Write the volume formula for a rectangular prism: length × width × height, then substitute 3, 4, and 6.

Volume tells how many cubic units fit inside a prism, so use all three dimensions. You can do 3 × 4 first for the base, then multiply by 6.

Solution walkthrough

01

Use the rectangular-prism volume formula

\[V=\text{lwh}\]

Volume equals base area length times width, extended through the prism's height.

02

Source the dimensions

\[l=3;~w=4;~h=6~\text{units}\]

The prism is three units long, four units wide, and six units high.

03

Substitute

\[V=(3)(4)(6)\]

Place each edge length into its corresponding factor.

04

Calculate and check units

\[V=12(6)=72~\text{cubic}~\text{units}\]

The twelve-square-unit base repeats through six layers, producing seventy-two unit cubes.

05

Report the volume

\[72~\text{cubic}~\text{units}\]

The rectangular prism contains seventy-two cubic units.

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Another way

  1. Find base area 3×4=12 square units, then multiply by height 6.

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Common mistake

Do not use the surface-area formula; volume multiplies all three perpendicular dimensions once.

Solution walkthrough video