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In mathematics, a prism can be defined as the surface which has flat bases of parallelogram and sides of the polygon. The total number of sides in a prism is equivalent to 6.
Thus, the surface area of a prism can be defined as the total region or area which is covered by the six sides of the prism. The mathematical formula given to calculate the surface area of a rectangular prism is categorized into types: the lateral surface and the total surface.
The formula given for the lateral surface is, 2 ( l + w or b ) + h where, ‘l’ is denoting length, ‘w’ or ‘b’ is the breadth or width of the rectangular prism and ‘h’ is the height of the prism. There are various types of prisms such as a rectangular prism, square prism, pentagonal prism, hexagonal prism, etc.
We shall try to cover some basic examples/calculations regarding the surface area of rectangular prisms so that you get conceptual clarity about the topic.
The Volume of a Rectangular Prism
In general terms, volume can be defined as the total space a shape occupies inside it. Likewise, the volume of a rectangular prism can be defined as the total amount of space that the rectangular prism can occupy.
The mathematical formula given to calculate the volume of a prism is, L * B or W * H, where, ‘l’ is the length of the prism, ‘b’ is the breadth of ‘w’ is the width and ‘h’ is the height of the rectangular prism.
You must remember that the resultant value is written in cubic units. For example, if you multiply 4 cm by itself thrice, the answer will be written as 16 cm cubic units. We will try to solve some examples based on the volume of rectangular prisms in the next section.
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Some Examples Based on the Volume of Rectangular Prism
As mentioned above, the formula given to calculate the volume of a prism is, L * B or W * H, where, ‘l’ is the length of the prism, ‘b’ is the breadth or ‘w’ is the width and ‘h’ is the height of the rectangular prism. Some of the examples are mentioned below:
Example 1: Calculate the volume of the prism if the given breadth, height, and length are 4 cm, 5 cm, and 8 cm respectively?
Solution: Given that,
The breadth of the rectangular prism = 4 cm
Height of the rectangular prism = 5 cm
Length of the rectangular prism = 8 cm
Using the formula for the volume of rectangular prism = l * b * h,
4 cm * 5 cm * 8 cm = 160 cm cubic units.
Therefore, the volume of rectangular prisms of the given measurements is equivalent to 160 cm cubic units.
Example 2: Find the volume of the prism if the given breadth, height, and length are 8 cm, 6 cm, and 4cm respectively?
Solution: Given that,
Breadth of the rectangular prism = 8 cm
Height of the rectangular prism = 6 cm
Length of the rectangular prism = 4 cm
Using the formula for the volume of rectangular prism = l * b * h,
8 cm * 4 cm * 6 cm = 192 cm cubic units.
Therefore, the volume of rectangular prisms of the given measurements is equivalent to 192 cm cubic units.
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Some Examples Based on the Lateral Surface Area of Prism
The formula for the lateral surface area of a rectangular prism is 2 ( l + b ) * h. Some of the examples are mentioned below,
Example 1: Calculate the lateral surface area of the prism, if the given measurement of length, width, and height are as follows: 4 cm, 7 cm, and 8 cm.
Solution: Given that,
Breadth of the rectangular prism = 7 cm
Height of the rectangular prism = 8 cm
Length of the rectangular prism = 4 cm
Using the formula of the lateral surface area of the rectangular prism is 2 ( l + b ) * h.
2 ( 4 + 7 ) 8 = 176 square units.
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