Volume of Cube, Cuboid and Cylinder

Cube, Cuboid, and cylinder form the part of 3D shapes. Generally, in a 3D shaped figure, you will find the measure of length, width, and height. On the contrary, in the case of a 2D figure, you have just the length and the height. Some of the examples of 2D shapes are triangle, square, and circle. Now,  let's look at what’s volume after all? Students generally have a hard time dealing with 3D figures. One of the reasons is their tendency to memorize formulae without actually understanding what it is. So, it would fare well to start with understanding what does the volume of any shape means?  

Reason for Difference Between Cube and Cylinder Volume

The volume of any 3D figure is the measure of the area enclosed by the area of the figure. In literal sense, Volume denotes the total capacity or the space occupied by the object which has all the three elements length, height, and width. The different formulas for each 3D shape are derived by the structure of formation. For instance, the structural difference between cube and cylinder introduces the need for a different formula of volume for each of the shapes in consideration.   

Cube

Cube is the first of 3D shapes which is quite tedious to map out. It is a figure enclosed by six identical squares. One of the interesting things about the cube is that a single vertex is formed at the meeting point of three edges. 

Cuboid

Just a heads up that any object which is in the form of a box is a cuboid. A cuboid essentially is a 3D shape that is characterized by six rectangular faces. Each vertex is formed at right angles. 

Cylinder 

The basic difference between cube and cylinder, structure-wsie lies in the presence of a third measure i.e height. The diet coke can which you might be holding in your hand while reading this article is an apt example of a cylinder.


A cylinder is a 3D shape, with two parallel sides with a circular or an oval opening at the top and the bottom. Now the openings can be hollow or in the solid-state.

How do you calculate the volume of Cube Cuboid and Cylinder

Calculating the volume of Cube, Cuboid, and Cylinder is quite straightforward provided you know the workarounds to arrive at the measurements of the figure at hand. 


The difference between cube and cylinder or cuboid and cylinder is quite stark. Also, cylinders do not belong to the polyhedron family of 3D shapes. The reason for its exclusion is mentioned in FAQs. Let us look at the volume of cube cuboid and cylinder individually.

 

The Volume of Cube

As mentioned earlier, a cube is formed of six identical squares. Thus, each side of the cube will have the same measurement. Now, for calculating the volume of a cube, you just need to find the cube of the given value of the side. 

For instance, if the measurement of the side is a then volume of a cube is i.e V= a


The Volume of Cuboid

The volume of the cuboid is the product of the length, breadth, and height, colloquially dubbed as ‘lbh’. For any cuboid of length L, Breadth B, and height H, the volume ‘V’ is equal to LxBxH.


The Volume of Cylinder

The volume of the cylinder involves the use of the area of the circle which is multiplied to the height. It is the easiest way to comprehend the formulae for the volume of a cylinder. 

For any cylinder with radius R and height H, the volume ‘V’ is represented as V= 𝚷 R2H.

Solved Examples

Now, we will see some of  the  solved examples of volume of Cube Cuboid and Cylinder

  1. Find the volume of a cube with side 9m?

Let the volume of the cube be V, Using the formulae V=a3, we have 

V= (9m)3 = 729

  1. Find the volume of the cuboid with length 12m, height 8m, and breadth 6m?

  Using the formulae for the volume of cuboid i.e V=LBH, we have, 

   V= (12X8X6)m3 = 576m3

  1. Find the volume of a cylinder with radius 14m and height 10m?

   Using the formulae for calculating the volume of cylinder i.e V=𝚷 R2H.

   We have, V= 22/7 x (14m)2 X (10m)= 6,160m3.

The volume of a cylinder with pythagoras theorem application to find actual height


  1. Find the volume of the cylinder with slant height 10cm and radius 3cm?


(Note- **slant height is the hypotenuse formed by joining the upper end of the oval opening to the opposite bottom end. For more clarity, see the figure below.)


As you can see in the slant height is denoted by d. Now, the formula for calculating the volume of the cylinder involves height. But in the question we do not have the value of height, thus, we have to calculate height using the Pythagorean theorem.


H2 (hypotenuse) = L2 (length) + B2 (breadth square) 


Similarly, here we have, d2=h2 + D2 (diameter)


(10cm)2= h2 + (6)2


Solving the above equation, we have h= 8cm


Now, V= 𝚷 R2

V= 22/7 x (3)2 x (8)


Solving the above equation we get V= 226 (approx).

Facts about Cube, Cuboid, and Cylinder

  • A square is often dubbed as the 2D substitute for the cube.  

  • A rectangular cuboid is quite similar to a cube, the main difference maker is that the cuboid does not have three edges of identical length.

  • Contrary to most 3D shapes which are polyhedron cylinder is not one of them. The reason for which the cylinder is not a polyhedron is the presence of surface area. 

FAQ (Frequently Asked Questions)

1. Can you turn a cuboid into a cube?

Yes, a simple mathematical approach can help us to know how many cuboids need to be fused to form a cube. 


For instance, consider the length, breadth, and height of a cuboid 5cm, 5cm, and 2cm respectively. Now the question is how many such cuboids are needed to form a cube.


Remember the volume in both cube and cuboid will be the same after the fusion. So, let us assume that n cuboids are required to form a cube with side p cm. 


The volume of ‘n’ cuboid = Volume of Cube with side p cm


(5X5X2)cm3 X n = (p)3


Solving the above equation you will conclude that 20 cuboids are required to form a cube.


2. Practical application of calculating the volume of Cube, Cuboid, Cylinder?

Though there is a stark difference between cube and cylinder or for that matter in any set of two 3D shapes, the concept of volume is universal. We are surrounded by 3D shaped objects and knowing the exact capacity in which each object saves a lot of time. 


Right from adding a simple detergent to the washing machine to fueling up the vehicle or storing water in a tank, the calculating volume is everywhere. The basic idea that we are trying to convey here is that the calculation of volume holds the key to various fields, and we remain aloof to most of them.