Online Volume of rectangular prism calculator
How to use the ‘Volume of a Rectangular Prism Calculator’?
Follow the following steps to use the volume of a rectangular prism calculator:
- Enter the known measures (i.e., any three from length, width, height or volume) into the respective input boxes and the unknown measure will be calculated.
- Select the appropriate units for the input and output.
- Now, click on ‘Solve’ to obtain the result.
- Click on the ‘Show Steps’ button to get the stepwise solution to find the missing measurement.
- Click on the
button to enter new inputs and start again. Click on the ‘Example’ button to play with different random input values.
When you click on the ‘Explore’ button you can see how the volume of the prism changes when the length, width, and height are varied.
- When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator.
What is the Volume of a Rectangular Prism?
A rectangular prism has six faces and all of them are rectangular in shape. The total amount of space occupied by a rectangular prism is called the volume of a rectangular prism.
Formulas used for the ‘Volume of Rectangular Prism Calculator’
The volume of the rectangular prism with length l, width w and height h can be written as:
Volume of the rectangular prism, \( V = l\times w\times h \)
Length of the rectangular prism, \( l= \frac{V}{w\times h} \)
Width of the rectangular prism, \( w= \frac{V}{l\times h} \)
Height of the rectangular prism, \( h= \frac{V}{w\times l} \)
How does the Volume change with a Unit Increase in Height?
Consider a rectangular prism of length ‘l’, width ‘w’, and height ‘h’.
Volume of rectangular prism, \( V=l\times w\times h \)
On increasing the height by a unit, the new height becomes \( h_1=h+1 \)
Hence, volume of rectangular prism \( V_1=l\times w\times h_1 \)
\( V_1=l\times w\times (h+1) \)
\( V_1=l\times w\times h+l\times w \)
\( V_1=V+l\times w\)
As a result, increasing the height of the prism by one unit increases the volume of the prism by length times the width of the prism.
Similarly, when any of the length, width, or height is incremented by a unit, keeping the other two units remaining the same; the volume increases by the product of the other two dimensions.
How many Unit Cubes make a Rectangular Prism?
Consider a rectangular prism of length l, width w, and height h made up of n number of unit cubes. A cube of side 1 unit is considered as a unit cube.
Volume of 1 unit cube \( =1^3=1 \) cubic unit
Volume of n unit cubes \( =n\times 1=n \) cubic units
If n unit cubes are filled in the rectangular prism, then
Volume of the rectangular prism = Volume of n unit cubes
\( l\times w\times h=n \)
Therefore, the number of unit cubes that can be filled in a rectangular prism is equal to the volume of the rectangular prism.
Solved Examples
Example 1: Find out the volume of a rectangular prism whose length, width, and height are 8 ft, 5 ft, and 4 ft respectively.
Solution:
\( V=l\times w\times h \)
\( V=8\times 5\times 4 \)
\( V=160 \) cubic feet
So, the volume of the rectangular prism is 160 cubic feet.
Example 2: Find out the length of a rectangular prism whose width, height, and volume are 6 cm, 5 cm, and 100 cubic centimeters, respectively.
Solution:
\( V=l\times w\times h \)
\( l=\frac{V}{w\times h} \)
\( l=\frac{100}{6\times 5} \)
\( l=3.333\ldots \) cm
So, the length of a rectangular prism is 3.333 cm.
Example 3: Find out the height of a rectangular prism whose length, width, and volume are 10 inches, 8 inches, and 480 cubic inches, respectively.
Solution:
\( V=l\times w\times h \)
\( h=\frac{V}{w\times l} \)
\( h=\frac{480}{10\times 8} \)
\( h=6 \) inches
So, the height of a rectangular prism is 6 inches.
Example 4: Find out the width of a rectangular prism-shaped box whose length, height, and volume are 4 feet, 3 feet, and 60 cubic feet, respectively.
Solution:
\( V=l\times w\times h \)
\( w=\frac{V}{l\times h} \)
\( w=\frac{60}{4\times 3} \)
\( w=5 \) feet
So, the width of the box is 5 feet.
As we know, the volume of a rectangular prism, V = l×w×h
If we double the dimensions, then the new volume = 2l×2w×2h
= 8×l×w×h
= 8V
Therefore, the volume of the rectangular prism increases by eight times.
A rectangular prism has six faces (4 lateral faces and 2 identical bases), eight vertices, and twelve edges.
A cube is a special type of rectangular prism, where the dimensions (length, width, and height) of the prism are equal.
Although both a cuboid and a rectangular prism have two identical rectangular bases and four lateral faces, all faces of a cuboid are perpendicular to each other. On the other hand, a rectangular prism may not have its faces perpendicular to each other. It may be oblique, or tilted to one side.