What Is the Volume of a Cuboid?
The volume of a cuboid is the quantity used to calculate the amount of space in a cuboid. A cuboid is a three-dimensional shape that we see all the time. Volume refers to the capacity of any shape based on its dimensions such as length, width, and height. A formula specific to the shape of a cuboid will be used to calculate its volume. In this section, we will learn how to calculate the volume of a cuboid and solve a few examples to better understand the concept.
What is the Cuboid's Volume?
The volume of a cuboid is the amount of space occupied by a cuboid. The cuboid is a three-dimensional shape with dimensions of length, width, and height. If we start with a rectangular sheet and keep stacking them, we'll get a shape with some length, breadth, and height. This stack of sheets resembles a cuboid because it has six faces, twelve edges, and eight vertices. (unit)3 is the unit of volume of a cuboid. The metric volume units are cubic meters or cubic centimeters, whereas the US Customary System (USCS) volume units are cubic inches or cubic feet. Because the volume of a cuboid is determined by its length, breadth, and height, changing any of those quantities changes the volume of the shape.
Cuboid Volume Formula
The formula for the volume of a cuboid can be derived from the rectangular sheet concept. Let 'A' be the area of a rectangular sheet of paper, 'h' be the height to which they are stacked, and 'V' be the volume of the cuboid. The volume of the cuboid is then calculated by multiplying the base area and height. The volume of a cuboid is equal to its base area multiplied by its height.
As a result, the volume of a cuboid, V = l b h = lbh
How to Determine the Volume of a Cuboid
The volume of a cuboid is the amount of space occupied within a cuboid. A cube is formed when all three dimensions of a cuboid are equal. The volume of a cuboid can be calculated using the cuboid volume formula. The steps for calculating the volume of a cuboid are as follows:
- Step 1: Determine whether or not the cuboids' dimensions are in the same units. If not, convert the measurements to the same units.
- Step 2: Once the dimensions are in the same units, multiply the cuboid's length, breadth, and height.
- Step 3: After obtaining the value, write the unit.
Let us use an example to learn how to use its formula to calculate the volume of a cuboid.
Find the volume of a cuboid with dimensions of 7 inches in length, 5 inches in width, and 2 inches in height.
The volume of a cuboid, V = lbh Here, length l = 7 inches, breadth b = 5 inches, and height h = 2 inches.
Thus, the volume of a cuboid, V = lbh = (7 5 2) in3.
⇒ V = 70 in3
As a result, the volume of the cuboid is 70 in3.
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Example 1: Assume the dimensions of a cuboidal fish aquarium are 30 inches, 20 inches, and 15 inches. Can you estimate the size of the fish aquarium?
As we all know, the fish aquarium has a cuboidal shape. As a result, the dimensions of the fish aquarium are as follows: aquarium length = 30 in aquarium width = 20 inThe aquarium's height is 15 inches.
The aquarium's volume is calculated as follows: Volume = Length Width Height
Volume = 30 20 15 in3 = 9000 in3
The volume of the cuboidal fish aquarium is 9000 cubic inches.
Example 2: What is the length of a cuboid with a volume of 3000 in3, a breadth of 15 inches, and a height of 10 inches?
As we all know, the volume of a cuboid is given as Volume = Length Breadth Height. The dimensions of a cuboid are as follows:
Volume = 3000 cubic inches, Breadth = 15 inches, and Height = 10 inches.
Assume that the length of the cuboid is x inches.
As a result, the volume of the cuboid will be as follows: Volume = Length Breadth Height
Volume = 15 x 10 = 3000 in3
⇒ x = (3000/(15 × 10)) = 20 inThe length of a cuboid is 20 inches.
Example 3: Determine the volume of a cuboid with dimensions of 10 in, 20 in, and 30 in.
Volume of a cuboid is given as Volume = Length Breadth Height. The dimensions of a cuboid are as follows: Length = 10 in Breadth = 20 in Height = 30 in
Volume = 102030in3=6000in3
The cuboid has a volume of 6000 cubic inches.
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Cuboid Volume Frequently Asked Questions
The volume of a cuboid is the space enclosed by a cuboid. For example, in order to fill an aquarium with water, we must first determine its volume.
How to Calculate the Volume of a Cuboid
A cuboid's volume is determined by multiplying its length, width, and height. The volume of a cuboid with dimensions of length, width, and height of 2 inches, 3 inches, and 4 inches is given as Volume = length width height = 2 3 4 = 24 inch3
What Is the Formula for Cuboid Volume?
A cuboid's volume is calculated as = Length Width Height. The volume of a cuboid is calculated by stacking rectangular sheets one on top of the other, yielding three parameters in the formula: length, width, and height.
How to Find the Volume of a Cuboid If the Dimensions of a Cuboid Are Different
If the units of the given dimensions of a cuboid differ, we must first change the units of any two dimensions in the unit of the third dimension. Then, multiply all three dimensions we know to find the volume of the cuboid.
Does the order of height, width, and length matter when calculating the volume of a cuboid?
No, the order of height, width, and length does not matter when determining the volume of a cuboid because we must multiply all three quantities to determine it. Because multiplication is associative, the volume of the cuboid remains constant regardless of the order in which the dimensions are multiplied.
How Does the Volume of a Cuboid Change When the Side Length Is Halved?
When the length of the side is halved, the volume of the cuboid is cut in half, as l = l/2. As an example, volume of cuboid = length width height = (l/2) b h = (lbh)/2 = volume/2 As a result, the volume of the cuboid is halved as soon as its length is halved.
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