## Volume of a Rectangular PrismIn geometry, a ## DefinitionA **Edge:**A-line segment connected with two vertices is called an**edge**. There are a total of**twelve**edges in a rectangular prism. These edges are of different lengths.**Face:**Faces are the rectangular sides of a rectangular prism. There are a total of**six**faces (top, bottom, right, left, front, and back) in a rectangular prism. The opposite faces are congruent.**Vertex:**A point where three edges meet or the corners of the shape is called the**vertex**. There are a total of**eight**vertices in a rectangular prism.
## Types of Rectangular PrismThere are two types of a rectangular prism: **Right Rectangular Prism:**A rectangular prism is a prism in which all the angles are right angles. In other words, a rectangular prism in which bases are perpendicular to each other is called the right rectangular prism. The following figure illustrates the shape of a right rectangular prism.**Oblique Rectangular Prism:**An oblique rectangular prism is a prism in which all the angles are not right angles. In other words, a rectangular prism in which bases are not perpendicular to each other is called the oblique rectangular prism. The following figure illustrates the shape of an oblique rectangular prism.
## Properties of Rectangular Prism- It forms a rectangular cross-section.
- It has
**six**rectangular faces,**twelve**edges, and**eight** - All the opposite faces are in rectangle shape.
- It is also a cuboid.
## Volume of Rectangular PrismThe space occupied by a three-dimensional object is called the The volume of a rectangular prism is the amount of space covered by a rectangular prism. In other words, ## Volume of Rectangular Prism FormulaThe volume of a rectangular prism is the product of Therefore, the volume of a rectangular prism can be written as: Volume of Rectangular Prism (V)=length×width×height Or Volume of Rectangular Prism (V)=l×w×h Let's see some examples based on the above formula.
Given, length (l) = 6 cm width (w) = 9 cm height (h) = 4 cm According to the formula: Volume of Rectangular Prism (V)=l×w×h Putting the values of l, w, and h in the above formula, we get: V=6×9×4
Given, length (l) = 2 m width (w) = 4 m height (h) = 9 m According to the formula: Volume of Rectangular Prism (V)=l×w×h Putting the values of l, w, and h in the above formula, we get: V=2×4×9
Look at the above figure, we see that it is a combination of two rectangular prisms. So, first, we will separate the figure into two rectangular prisms. After that, we will find the volume of both prisms, and at last, add both volumes to find the volume of the entire figure. Let's separate the prisms, we get the following two figures. Now, we will calculate the volume of both prisms, separately. First, we will calculate the volume of the According to the formula: Volume of Rectangular Prism (V)=l×w×h Putting the values in the above formula, we get: V=12×9×2 Now we will calculate the volume of the V=12×2×6 Add both the volumes to find the volume of the V=216+144
In the given figure: The length of the prism is: The width of the prism is: The height of the prism is: According to the formula: V=l×w×h Putting the values in the above formula, we get: V=6×3×4
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