What is a Cuboid?
A cuboid is a three-dimensional form in geometry. A cuboid is a convex polyhedron surrounded by 6 rectangular faces, each with 8 vertices and 12 edges. A rectangular box is an example of a cuboid in real life. Other forms that are precisely like a cuboid may be found in mathematics. A cuboid is a hexagon in geometry. It has a rectangular face. "Cuboid" implies "like a cube" in the sense that you can change the length of the edges or the angle between the edges and faces to make it a cube. A cuboid is a convex polyhedron having the same polyhedral graph as a cube in mathematics.
Volume of Cuboid: Meaning
The cuboid is the three-dimensional equivalent of the two-dimensional rectangle. The cuboid is generated when a rectangle is rotated about its axis. A rectangular prism is another name for the cuboid. A cuboid's volume is the area occupied by the cuboid form.
Volume of Cuboid
The volume of a cuboid is the quantity used to measure the amount of space in a cuboid. Volume refers to the capacity of any form depending on its measurements, such as length, width, and height. A formula particular to the shape of a cuboid will be employed to compute its volume. In other words, we want to figure out how big this box is. The volume of a cuboid is the amount of space occupied by a cuboid.
Volume of Cuboid Properties
Before learning about various cuboid amounts, it is necessary to understand the attributes of a cuboid, so that we can readily detect a cuboid based on its properties.
The primary qualities of a cuboid are stated below-
- A cuboid has six faces, eight vertices, and twelve edges.
- The edges on either side are parallel to each other.
- Because a cuboid is a three-dimensional object, it possesses length, width, and height.
- A cuboid has only right angles at its vertices.
- All of the faces are rectangles.
- A cuboid contains two diagonal lines that may be drawn on each face.
Read more about the Formula of CSA of Cylinder, TSA of Cuboid and Perimeter of Cuboid.
Volume of Cuboid Formula
The formula for the volume of a cuboid may be obtained from the rectangular sheet notion.
Cuboid volume = Base area x Height |
The base area of a cuboid is equal to l x b.
As a result, the volume =
V = l x b x h |
Other Related Formulas
Here's a collection of all cuboid-related formulae in one location. We examined a cuboid with the measurements length (l), height (h), and breadth (b)-
Cuboid's Quantities | Formulas |
Perimeter | 4(l + b + h) units |
Lateral Surface Area (LSA) | 2h(l + b) sq.units |
Total Surface Area (TSA) | 2(lb + bh + hl) sq.units |
Volume | l × b × h cubic units. |
Face Doiagonals | √(l² + b²) units |
Space Diagonal | √(l²+ b²+ h²) units |
Also Read- What is the Area of a Parallelogram?
How to Find the Volume of a Cuboid?
The volume of a cuboid is the amount of space occupied by a cuboid. A cube is formed when all three dimensions of a cuboid are equal. The volume of a cuboid may be computed using the volume of a cuboid formula. The procedures for calculating the volume of a cuboid are as follows-
Step 1: Determine if the dimensions of the cuboids are in the same units. If not, convert the measurements to the same units.
Step 2: Once the measurements are in the same units, double the cuboid's length, width, and height.
Step 3: After obtaining the value, write the unit.
For example:- Find the volume of a cuboid with dimensions of 7 inches long, 5 inches wide, and 2 inches high.
We all know that the volume of a cuboid, V = l x b x h
In this case, l = 7 inches, b = 5 inches, and h = 2 inches.
Thus, the volume of a cuboid, V = l x b x h = (7 x 5 x 2) in3
V = 70 in3
A cuboid has a volume of 70 in3.
Also read more about- Difference Between Cube and Cuboid.
Types of Cuboids
The following table gives details about the types of cuboids that are classified into two types-
Solid Cuboid | Hollow Cuboid |
A solid cuboid is a three-dimensional object in the shape of a cuboid that is filled with the material it is constructed of. Consider the case of bricks. | A hollow cuboid is a cuboid with only the exterior cubical wrapping and nothing filled inside. |
How to Determine the Cuboid's Shape
Six faces, eight vertices, and twelve edges make up the cuboid. A cuboid's faces are all rectangles. The basic parameters of three-dimensional objects, such as the face, vertex, and edge, are explained below-
- Faces: All distinct flat surfaces of a solid item are referred to as the object's faces. A cuboid is a shape with six rectangular faces.
- Edge: A line segment that links two vertices is referred to as an edge.
- Vertex: A vertex is a point at which two or more lines intersect. A cuboid's vertex is the place where two edges meet. A corner is also known as a vertex. A cuboid has twelve edges, yielding eight vertices.
Also read more about the- Father of Mathematics.
Uses of Cuboid
Understanding the volume of a cuboid is useful in many ways. There are several items that we utilize on a daily basis. These include various types of boxes, metal cuboids, and so on. All of them are cubes. However, they differ in size and texture. The sides of the cuboids determine the size of the cuboids. Steel or metal cuboids are also employed for a variety of industrial uses. Calculating the mass of anything requires information about the volume.
Also read more about the Difference Between Fraction and Rational Number.
Things to Remember
The following are some things to remember about cuboids:-
- A cuboid is a geometrical shape with six quadrilateral faces.
- The volume of a hollow cuboid is defined as the cuboid's capacity.
- Each cuboid face has a distinct rectangular form, implying that each cuboid face is a rectangle.
- An adjacent face of a cuboid is any two faces of the cuboid that are not opposing.
- A cuboid's volume may be determined as the product of its length, width, and height.
- Out of the six faces of the cuboid, anyone face can be characterized as the cuboid's base.
- In general, the face on which a solid must rest is the cuboid base.
- An edge is a line segment that connects any two adjacent vertices.
- The cuboid has 12 equally spaced edges.
- A vertice is the point where three edges intersect.
- A cuboid has eight vertices in total.
Questions for Practice
Q.1 Determine the volume of a cuboid with the following dimensions-
- 45 cm in length, 10 cm in width, and 62 cm in height.
- 97 m in length, 43 m in width, and 53 m in height.
- 4.2 m in length, 2.9 m in width, and 2.5 m in height.
- 94 cm in length, 46 cm in width, and 69 cm in height.
- 1.9 m in length, 6.5 m in width, and 7 m in height.
Q.2 Michael constructed a shoe box that was 8 cm long, 6 cm wide, and 6 cm tall. Determine the box's volume.
Q.3 Determine the number of cubical boxes with cubical sides of 3 cm that may be accommodated in a carton with dimensions of 15 cm x 9 cm x 12 cm.
Q.4 Determine the volume of a cuboid with dimensions of 17 mm x 0.2 cm x 12 mm in cu. cm.
Q.5 Determine the volume of a cuboid with dimensions of 14 cm x 12 cm x 8 cm.
Q.6 A fish tank measures 40 cm in length, 15 cm wide, and 10 cm tall. What is its volume in cubic centimeters?