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The volume of the cuboid: The volume of the cuboid is precisely the total space covered by the cuboid in a 3D space. Cuboid is a 3D shape. It has six blockish or rectangular faces. These six faces make three couple of parallel faces. Thus, the volume of the cuboid is measured based on the dimension of these faces, i.e. the length, breadth and height.
Volume of a Cuboid= Length * Breadth * Height
What is the volume of a Cuboid?
The volume of a cuboid is precisely the total space enthralled by the cuboid in a 3D space. The conception of calculating the volume of a cuboid is abecedarian in figure. This fine conception of calculating the volume of different 3D numbers is essential in fields similar as drugs, engineering, and armature.
The volume of a cuboid is determined by multiplying its confines length(l), range or breadth(w), and height(h), expressed by the formula
V = length × width × height( lwh) boxy units or units3
Also, a cuboid is occasionally called a solid cube. It’s because all the faces of a cuboid are blocks.
Volume of Cuboid Formula
The volume of a cuboid is determined by the product of its confines or dimensions. By multiplying its confines, length( l), range( w), and height( h), we get the formula:
V = length × range × height( lwh) boxy units
The unit of volume of cuboid is expressed in boxy units similar to metre3, centimetre3 and further.
Consider a practical illustration with a cuboid measuring 5 units in length, 3 in range, and 2 in height.
Applying the formula, we get the Volume of a Cuboid as
V = length × width × height( lwh)
V = 5 * 3 * 2 = 30 boxy units.
Thus, the performing volume is 30 boxy units.
How do you find the Volume of the Cuboid?
The volume of a cuboid is a precise calculation of the space it takes up inside. Now, you must figure out how much sugar can easily fit inside this box. Therefore, you want to find the box’s volume for this purpose. The capacity of a box is the same as its volume. So, if you know the length, width, and height of the box, you can find the volume using this simple formula:
Volume of the box = Length x Width x Height
Here’s a step-by-step guide to finding the volume of any cuboid:
Step 1: Look at the measurements of the cuboid, which are the length, width, and height.
Step 2: Check if all these measurements have the same units. If not, make them the same.
Step 3: Once all measurements have the same units, multiply the length, width, and height together.
Step 4: The result you get is the volume of the cuboid, and it’s usually expressed in cubic units.
How to Calculate a Cuboid’s Total Surface Area and Lateral Surface Area?
The total surface area of a cuboid is the combined area of all six of its rectangular sides. On the other hand, the lateral surface area includes only four sides, excluding the top and bottom faces. Here are the formulas for both:
Total Surface Area of a Cuboid
Total Surface Area = 2(lb + hb + lh) square units
Lateral Surface Area of a Cuboid
Lateral Surface Area= 2h(l + b)
- For total surface area, you add the areas of all six faces: length times breadth (lb), height times breadth (hb), and length times height (lh), and then multiply the sum by 2.
- For the lateral surface area, you consider only the four sides, excluding the top and bottom faces. Multiply the height (h) by the sum of length (l) and breadth (b), and then multiply the result by 2.
These formulas help you find how much space the cuboid covers on its surfaces. Understanding these concepts is crucial before diving into the detailed discussion of the cuboid’s volume.
How to Find the Volume of a Cuboid Prism and a Cube?
A cuboid prism, also known as a rectangular prism, is like a regular cuboid. It has six faces, eight vertices, and twelve edges. When its cross-section is rectangular, it is called a right prism, meaning the angle between the base and sides is at right angles. The top and bottom surfaces are identical in shape and size. Now, let’s get to finding their volumes:
Volume of a Cuboid Prism or Rectangular Prism:
V = length*breadth*height cubic units
This formula helps calculate the amount of space the cuboid prism occupies inside.
Volume of a Cube
A cube is a specific type of cuboid where all sides have equal lengths. The formula for its volume is simpler:
Volume of a cube with side ‘a’ = a3
Here, ‘a’ represents the length of each side.
Understanding these formulas allows you to determine how much space is enclosed within these geometric shapes, whether it’s a general cuboid prism or a cube with equal side lengths.
Solved examples on Volume of Cuboid
Q1. Find the volume of a cuboid whose length, width and height are 10cm, 5cm and 2cm, respectively.
Ans. The volume of cuboid = Length x Width x Height
V = 10 * 5 * 2 = 100 cm cube
Q2. Find the volume of a box whose length, width and height are 20, 3, and 2, respectively. And let the unit be measured in centimetres.
Ans. The volume of cuboid = Length x Width x Height
V = 20*3*2 = 120 cm cube
Practice questions on the Volume of the Cuboid
Q1. Find the volume of a shoe box whose length, width and height are 15, 12, and 5, respectively. And let the unit be measured in centimetres.
Q2. Find the volume of a cuboidal box whose length, width and height are 18, 6, and 3, respectively. And let the unit be measured in metres.
FAQs on Volume of Cuboid
What is the formula for the Volume of the Cuboid?
The formula of the volume of a cuboid = Length x Width x Height
What is the unit of volume of a cuboid?
The unit of the volume of a cuboid is a cubic unit. It can be metres3, centimetres3 and more.
Define the volume of a cuboid?
The volume of a cuboid is precisely the total space occupied by the cuboid in a 3D space. It is calculated by the formula Length x Width x Height.
