A prism can be defined as a polyhedron that has identical bases, rectangular bases that are flat, and the same cross-section along its length of it. It is further classified into various types based on its bases of it. Bases can be either triangular or rectangular. A rectangular prism is a type of prism which is made up of six congruent rectangular bases. It is also considered a three-dimensional shape as it had all three dimensions i.e. length, breadth, and height. The volume of rectangular prism can be defined as the total region or area occupied by the rectangular prism inside it. We can also regard it as the total amount of cubic units, a rectangular prism can hold. The mathematical formula given to calculate the volume of a rectangular prism is l * w * h where ‘l’ is the length, ‘h’ is the height and ‘w’ is the width of a rectangular prism. In this article, we shall cover some topics related to the volume of prisms such as the volume of a triangular prism, examples based on it, and many others in a detailed and effective manner.
Examples
To recall, the formula given to calculate the volume of a rectangular prism is l * w * h where ‘l’ is the length, ‘h’ is the height and ‘w’ is the width of a rectangular prism.
Example 1: Find the volume of a rectangular prism if the dimensions of length, width, and height are 4 cm, 8 cm, and 12 cm respectively.
Solution:
Given that,
Length of the prism = 4 cm
The breadth of the prism = 8 cm
Height of the prism = 12 cm
Using the formula of the volume of rectangular prism = l * b * h.
4 * 12 * 8 = 32 * 12
32 * 12 = 384 cm cubic units.
Hence, the volume of the rectangular prism is 384 cm cubic units.
Example 2: Find the volume of a rectangular prism if the dimensions of length, width, and height are 5 cm, 10 cm, and 12 cm respectively.
Solution:
Given that,
Length of the prism = 5 cm
The breadth of the prism = 10 cm
Height of the prism = 12 cm
Using the formula of the volume of rectangular prism = l * b * h.
5 * 10 * 12 = 50 * 12
50 * 12 = 600 cm cubic units.
Hence, the volume of the rectangular prism is 600 cm cubic units.
Volume of the Triangular Prism
As mentioned above, a prism is categorized on the basis of its identical bases of a prism. If the bases are rectangular, it is known as a rectangular prism. Likewise, when the bases are triangular, it is known as a triangular prism. However, a triangular prism is made up of rectangular faces as well. It consists of three triangular faces and 2 rectangular lateral faces. Now, the volume of triangular prism is the total space occupied by the prism inside it. The resultant value is always written in cubic units. Thus, a triangular prism can be considered a three-dimensional figure. The mathematical formula to calculate the volume of triangular is the product of the area base and its length or a * l where ‘a’ is the area of the base and ‘l’ is the length of the prism. The area of the base is different for various prisms. For instance, the area of the base is different for an equilateral triangle than that of a right-angled triangle. We shall solve and try to attempt some questions regarding the volume of the triangular prism in the coming sections.
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