Volume of a Cuboid Formula
In geometry, a cuboid is a three-dimensional shape. A convex polyhedron surrounded by 6 rectangular faces with 8 vertices and 12 edges is called a cuboid. A cuboid with 6 square faces is called a cube. An example of a cuboid in real life is a rectangular box.
In mathematics, we can observe other shapes that are exactly like a cuboid. In geometry, a cuboid is a hexagon. Its face is a rectangle. “Cuboid” means “like a cube” in the sense that you can convert a cuboid into a cube by adjusting the length of the edges or the angle between the edges and faces. In the language of mathematics, a cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.
What is a Cuboid?
A cuboid is a 3D solid with 6 faces (rectangles), 8 vertices, and 12 edges. A cuboid has three dimensions: length, width, and height. A perfect cuboid is a cuboid with integer edges.
We know that a rectangle is a two-dimensional figure with four sides. Now imagine the shape formed when many congruent rectangles are placed on top of other rectangles. This shape is called a cuboid. Notice the following cuboid showing three dimensions: length, width, and height.
Shape of Cuboid
The shape of a cuboid is a closed 3D shape surrounded by a rectangular surface, that is, a flat area of ​​a rectangle. The shape of the cuboid is shown in the figure below.
Cuboid
Volume of Cuboid
The volume of a cuboid is the total space that the box occupies in three-dimensional space. A cuboid is a three-dimensional structure with six rectangular faces. These six faces of a cuboid exist as a pair of three parallel faces. Therefore, volume is a measure based on the dimensions of these faces: length, width, and height. It is measured in cubic units.
Volume of cuboid = length × width × height (cubic unit)
How to calculate the volume of a cuboid?
The volume of a cuboid is the space it occupies inside the cuboid. A cuboid is a cube if all three dimensions of a cuboid are equal. The volume of a cuboid can be calculated using the cuboid volume formula. Steps to calculate the volume of a cuboid:
Step 1: Check that the dimensions of the given cuboid are in the same units. If not, convert the dimensions to the same units.
Step 2: Multiply the length, width, and height of the cuboid when the dimensions are in equal units.
Step 3: After you get the value, record the unit at the end.
Sample Questions
Question 1: How to find the length of a cuboid?
Answer:
The volume of a cuboid is equal to length × width × height.
Given the volume, width, and height,
We can write
v = l×b×h
⇒ l=v/bh
Question 2: Does the order of the cuboid matter for volume calculations?
Answer:
It doesn’t matter whether you hold the cuboid vertically or horizontally. The volume of a cuboid is the same even if you change the order of length, width, and height.
Question 3: If you cut the length of one side by half, how will the volume of the cuboid change?
Answer:
The volume of a cuboid is l = l/2, so if you cut the length of one side by half, it is halved.
Because volume = length × width × height
= (l/2) × b × h
= (lbh)/2
= volume/2.
Thus, the volume of a cuboid is halved as soon as its length is halved.
Question 4: If a cube has a volume of 3000 cm3, a width of 10 cm, and a height of 10 cm, what is the length?
Answer:
The volume of a cuboid is Volume = length × width × height
The dimensions of a cuboid are as follows:
Volume=3000 cm3
Width=10 cm
Height=5 cm
The length of the cuboid =x cm.
So the volume of a cuboid is,
Volume=h×10×5=3000
h=3000/50
=60 cm.
The length of a cuboid is 60 cm.
Question 5: Cuboidal fish tanks have dimensions of 30 inches, 20 inches, and 15 inches. Can you determine the volume of an aquarium with fish?
Answer:
Given that,
The Length of the aquarium = 30 inches
The Width of the aquarium = 20 inches
The Height of the aquarium = 15 inches
Since the volume of the aquarium is expressed as:
Volume = Length × Width × Height
= 30 × 20 × 15 inches3 = 9000 inches3
Thus, the tank has a volume of 9000 cubic inches.
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