Volume Of Cuboid

A cuboid is a fundamental geometrical figure that is used in many everyday objects like cardboard boxes, bricks, and wooden beams. A cuboid is a three-dimensional complex polyhedron that has six faces, twelve edges, and eight vertices. Each face of a cuboid is a rectangle. A cube, on the other hand, is a three-dimensional shape that has six square faces. 

It is important to understand the volume of cube and cuboid to not only solve mathematical problems but also navigate practical tasks like calculating storage capacity or architecture that often involve designing cubic-shaped rooms, windows, and furniture. In this blog, we will walk you through the cuboid volume formula and provide examples and exercises for you to understand the concept in a more detailed manner. 

1.0What is a Cuboid?

In simple terms, a cuboid is a three-dimensional geometric shape that has six rectangular edges, eight vertices, and twelve edges. It looks like a rectangular box, which means each rectangular face meets at right angles. The opposite faces are the same shape and size. Below is a picture of the cuboid shape to understand it better:

In simpler terms, imagine there is a rectangular box or object. It has height, width, and length. The space inside the box is the volume of the cuboid. Finding out the volume of the cuboid essentially means we are finding out the space occupied within the cuboid. 

2.0Cuboid Volume Formula

The volume of a cuboid is a byproduct of its dimensions, which are the length, width, & height. The unit of its volume is in cubic units or unit³, such as cm³, m³, in³, etc. 

The volume of a cuboid is equal to the base area multiplied by the height. 

The volume of any given cuboid = Base area × Height  [Cubic units]

However, the base of cuboids is rectangular in shape. So, the base area of cuboids is equal to the product of the length(l) & breadth(b) of the rectangle. The ultimate cuboid formula for volume would be:

Volume of any cuboid = length × breadth × height    [cubic units]

The volume of a cuboid = lbh  [cubic  units]   

Here, “l” stands for the length, “b” stands for the breadth, and “h” stands for the height. 

Let’s look at a quick problem to understand the cuboid volume formula in depth. For example, if a cuboid has a length of 5cm, a breadth of 3cm, and a height of 2cm, what would the volume be?

Volume = 5 cm × 3 cm × 2 cm = 30 cm³

Thus, the cuboid occupies 30 cubic centimetres of space.

3.0Difference Between the Volume of a Cube and a Cuboid

The key difference between the volume of a cube and cuboid is that in the case of a cube, it has all equal sides. So, the volume of a cube is calculated by multiplying one side by three. While a cuboid is made out of rectangles and has different lengths for its sides. So, the volume of the cuboid is calculated by multiplying the height, length, and width. 

So, the cube volume formula is: 

Volume= Side³ unit³

The cuboid volume formula is: 

Volume = length × breadth × height unit³

The volume of the cube and cuboid formula is essentially the same. In the case of cubes, the formula is a simplified version of the cuboids where all dimensions are the same. 

4.0Cuboid Volume Calculator

If you do not want to manually calculate the volume of a cuboid, many cuboid volume calculators simply allow you to put the values of the height, length, and width to get an accurate result. You typically need to provide the correct unit ((like centimetres, meters, or inches) for the dimensions to get the correct volume unit (cubic centimetres, cubic meters, cubic inches). This is commonly used by professionals, students, and engineers as part of a large sum. 

5.0Volume of a Cuboid Worksheet

One of the best ways to understand a concept thoroughly is by practice. Our volume of a cuboid worksheet has multiple problems of all difficulty levels that would help you understand the volume of cuboid questions. 

Question 1: Find the volume of a cuboid whose length = 5 cm, width = 2 cm and height = 3 cm.

Solution: 

Volume = l × b × h

Volume = 5 × 2 × 3 = 30 cm³.

Question 2: A rectangular box has a length of 10 meters, a width of 4 meters, and a height of 3 meters. What is the volume of the box in cubic meters?

Solution: 

Volume = l × b × h

Volume = 10 × 4 × 3 = 120 m³.

Question 3: A cuboid is 15 cm long, 4 cm wide, and 7 cm high. Calculate the volume.

Solution: 

Volume = l × b × h

Volume = 15 × 4 × 7 = 420 cm³.

Question 4: A cuboid has a volume of 240 cm³, a length of 10 cm, and a width of 4 cm. What is the height of the cuboid?

Solution: 

Volume = l × b × h

To find the height, rearrange the formula to Height = Volume/(Length x Width)

Height = 240/(10 × 4) = 6 cm. 

Question 5: The volume of a cuboid is 1.2 m³. If the length is 2 meters and the width is 3 meters, what is the height of the cuboid?

Solution: 

To find the height, rearrange the formula to Height = Volume/(Length x Width)

Height = 1.2/(2 ×3) = 0.2m. 

6.0Volume of Cuboid Examples: Real-Life Applications

The volume of cuboid examples can be seen in real-life applications. Here are a few examples where the cuboid formula may be useful. 

• Packing and Shipping: When packing and shipping, companies often calculate the volume of the boxes to see how much space they will take up.
• Construction: Calculating the cuboid structures is needed to determine the amount of materials needed for construction. 
• Storage Solutions: For warehouses and storage, knowing the volume of cuboid structures can help organise products and maximise space. 

7.0Conclusion

The cuboid volume formula is straightforward and easy to understand. By practising the volume of a cuboid worksheet, you can easily solve mathematical and real-life problems. Go through the basic concepts and apply them in the worksheets to perfect the area.