Volume of a Rectangular PrismIn geometry, a rectangular prism is a polyhedron (the shape whose all sides are flat) with two congruent and parallel bases. It is called prism because it forms a crosssection along the length. In this section, we will discuss the definition of a rectangular prism, types, volume formula, and the volume of a rectangular prism. DefinitionA rectangular prism is a threedimensional solid shape that has six rectangular faces. Another name of the rectangular prism is cuboid. It has twelve edges, six faces, and eight vertices. Brick, box and book are the best examples of the rectangular prism. The following figure illustrates the shape of a rectangular prism.
Types of Rectangular PrismThere are two types of a rectangular prism:
Properties of Rectangular Prism
Volume of Rectangular PrismThe space occupied by a threedimensional object is called the volume of that object. The volume of a rectangular prism is the amount of space covered by a rectangular prism. In other words, the number of units used to fill a rectangular prism is called the volume of a rectangular prism. The unit of volume is the cubic unit or unit^{3}. Volume of Rectangular Prism FormulaThe volume of a rectangular prism is the product of length (l), width (w), and height (h). It is denoted by V. 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. Example 1: Calculate the volume of the following rectangular box. Solution: 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 Hence, the volume of the given rectangular prism is 216 cm^{3}. Example 2: If the length, width, and height of a rectangular prism is 2 m, 4 m, and 9 m, respectively. Find the volume of the rectangular prism and also draw the figure. Solution: 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 Hence, the volume of the rectangular prism is 72 m^{3}. Example 3: Find the volume of the two prisms, separately, and also find the volume of the entire figure. Solution: 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 green color figure. 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 orange color figure. V=12×2×6 Add both the volumes to find the volume of the entire figure. V=216+144 Hence, the volume of the entire figure is 360 cm^{3}. Example 4: Find the volume of the prism given below. Solution: In the given figure: The length of the prism is: 6 units The width of the prism is: 3 units The height of the prism is: 4 units According to the formula:
V=l×w×h
Putting the values in the above formula, we get: V=6×3×4 Hence, the volume of the rectangular prism is 73 units^{3}.
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