Table of Contents
What is Meant by Volume?
Volume is easily defined as the amount of space occupied by any three-dimensional solid. These solids can be cubes, cuboids, cones, cylinders, or globes.
Different shapes have different volumes. In 3-D geometry, we have studied various shapes and solid objects such as cubes, cylinders, cones, cuboids and so on, described in three dimensions.
What is a Rectangular Prism?
A rectangular prism is a three dimensional shape of a hexagon (2 tops, 2 bottoms, 4 sides). All of the prism’s faces are rectangular. As a result, there are three pairs of identical faces in this picture. A rectangular prism is also known as a cuboid because of its shape. A rectangular prism can be found in a geometry box, notebooks, diaries, rooms, and other places. The shape of a rectangular prism can be seen in the diagram below.
Read more:
Examples of Rectangular Prisms in Real Life
A rectangular prism can be found in a truck, a chest of drawers, and an aquarium, among other place
Formula for the Volume of a Rectangular Prism
The occupied units of a rectangular prism are measured by the volume of the prism. Cubic units are used to represent the volume of a rectangular prism. The number of units used to fill a rectangular prism is also defined.
The area of the base multiplied by the height equals the volume of the rectangular prism.
A rectangular prism’s volume is equal to the multiplication of its length, width, and height in cubic units.
\(=l\times~w\times~h \) cubic units of volume
Where l is the length, w is the width, and h is the height of the rectangular prism.
How do You Calculate the Volume of a Rectangular Prism
Before using the formula to calculate the volume of a rectangular prism, make sure that all of the dimensions are in the same units. The volume of a rectangular prism is calculated using the steps below.
Step 1: Determine the type of base and its area using an appropriate formula (as explained in the previous section).
Step 2: Determine the prism’s height, which is perpendicular to the prism’s top vertex and base.
Step 3: To calculate the volume of the rectangular prism in cubic units, multiply the base area by the height of the prism. The volume of a prism is equal to the base area multiplied by the prism’s height.
Read More: Volume of a rectangular prism calculator
Solved Challenges on Volume of a Rectangular Prism
Volume of Rectangular Prism Examples
Example 1:
Calculate the volume of a rectangular prism with dimensions of 8 ft, 5 ft, and 4 ft, respectively.
Solution:
Given that:
Length, \(l= 8ft\)
Width, \(w= 5ft\)
Height, \(h= 4ft\)
The formula for calculating the volume of a rectangular prism is as follows:
Volume = Length x Width x Height cubic units
Volume = \(8\times~5\times4 \) cubic feet
Volume = 160 cubic feet
As a result, a rectangular prism’s volume is 160 cubic feet.
Example 2:
The bed of a dump truck is shaped like a rectangular prism. The base is 8 square yards in size. It stands at a height of 2 yards. How much gravel can it transport at once?
Solution:
Use a formula to calculate the volume of the dump truck bed.
Volume = Base area × height [Formula for volume of a rectangular prism]
= 8 × 2
= 16 cubic yards
The volume of the dump truck bed is 16 cubic yards.
So, the driver can transport 16 cubic yards of gravel at a time.
Example 3:
The volume of the rectangular prism is 72 cubic feet. Find the height.
Solution:
V = Area of Base × height formula for the volume of a rectangular prism
\(72=9\times~h\) write an equation
\(72\div~9=h\) write the related division equation
8 = h divide 72 by 9
The height is 8 feet.
Example 4:
The candle has a volume of 640 cubic centimetres. Will the candle fit inside the glass jar completely? Explain.
Solution:
Use a formula to find the height of the candle.
\(V=B\times~h\) formula for volume of a rectangular prism
\(640=40\times~h\) write an equation
\(640\div~40=h\) write the related division equation
\(16=h\) divide 640 by 40
The height of the candle is 16 feet.
Compare the base area and height of the candle and the glass jar:
Base area of the glass jar is greater than the candle.
And the height of the glass jar is less than the candle’s height.
So, the candle cannot fit inside the glass jar completely.
The volume of a rectangular prism refers to the amount of material it can hold or the amount of space it takes up. A rectangular prism’s volume can thus be calculated by multiplying its base area by its height.
Volume (V) = height of the prism × base area is the formula for calculating the volume of a rectangular prism.
Volume (V) = Area of base × height of the prism is the formula for calculating the volume of a rectangular prism.
Volume = l × w × h is another way to express this formula, where ‘l’ is the length, ‘w’ is the width, and ‘h’ is the prism’s height.
Volume is measured in cubic units such as cubic feet, cubic inches, cubic yards, and so on.