Question

Draw a rectangular prism that is 4 centimeters by 8 centimeters by 3 centimeters. Find the volume of the prism.

Short answer

The volume of the rectangular prism is 96 cm³.

Step-by-step solution

Understand the Problem

The problem requires us to find the volume of a rectangular prism with specific dimensions: 4 cm by 8 cm by 3 cm. Drawing it is not necessary for finding the volume, but knowing the dimensions is crucial.

Recall the Formula for Volume

The volume of a rectangular prism is calculated using the formula:\[ V = l \times w \times h \]where \( l \), \( w \), and \( h \) are the length, width, and height of the prism, respectively.

Substitute Values into the Formula

We substitute the given dimensions into the formula. Here, \( l = 4 \) cm, \( w = 8 \) cm, and \( h = 3 \) cm. So the formula becomes:\[ V = 4 \times 8 \times 3 \]

Calculate the Volume

Perform the multiplication: \( 4 \times 8 = 32 \) cm², and then \( 32 \times 3 = 96 \) cm³.Thus, the volume of the rectangular prism is 96 cubic centimeters.

Key concepts

Rectangular Prism

A rectangular prism is a three-dimensional shape that has six faces, all of which are rectangles. It resembles a box or a cuboid.
Each edge of a rectangular prism is either parallel or perpendicular to the others, forming right angles. The structure can easily be imagined as a rectangular piece of building block. Understanding this will help you visualize how its volume is calculated.

• Edges: 12
• Vertices: 8
• Faces: 6 rectangle faces

When studying rectangular prisms, we are mainly interested in three measurements: the length, the width, and the height. These dimensions allow us to calculate its volume, which describes the space contained within the prism.

Volume Calculation

Volume is a measure of how much space an object occupies. For a rectangular prism, calculating volume is straightforward. You need three measurements: length, width, and height.
The formula to find the volume of a rectangular prism is:\[ V = l \times w \times h \]Where:

• \( V \) = Volume
• \( l \) = Length
• \( w \) = Width
• \( h \) = Height

Using this formula, you multiply the three dimensions together. It's like stacking rectangle layers to see how much space it fills up.

Geometric Formulas

Geometric formulas are essential tools that help us solve problems related to shapes and sizes. They include formulas for calculating areas, volumes, and even perimeters.
For a rectangular prism, the volume formula provides a useful way to quantify the three-dimensional space it occupies. It's helpful to remember these important points:- The formula \( V = l \times w \times h \) is specific to rectangular prisms.- Rectangular prisms are among the simplest 3D shapes, making their formula relatively easy to use and understand.- This formula is linear; changing any single dimension while keeping others constant will proportionately affect the volume.Studying geometric formulas allows you to apply mathematical reasoning to real-world situations, solving various spatial problems effectively.