Volume of Cylinder

The volume of the cylinder is the space it occupies. It can be calculated by using the formula 

V = ℼr²h.

Here, r is the radius of the circular base.

h is the height of the cylinder.

ℼ is approximately 3.14159.

In real life, the cylinder volume is used in geometry, engineering, etc.
 

We use the following ways to find the volume of the cylinder. 

1. Volume of cylinder with height and radius.
2. Volume of cylinder with height and diameter.
3. Volume of cylinder with slant height.
    

By substituting the values of height and radius of the given cylinder in the formula V = ℼr2h, we can find the volume of the cylinder. 

Example: Find the volume of a cylinder with a radius 5 cm and height 10 cm.

Given, radius (r) = 5

Height (h) = 10

Using the formula, V = ℼr²h

V = 3.14159 × 5² × 10 

= 3.14159 × 25 × 10 

= 785.4 
 

When the diameter of the cylinder is given instead of the radius, we need to change the formula to r = d/2.

Therefore, the formula becomes V = ℼ(d/2)²h.

Let’s see this using a simple example, find the volume of a cylinder with a diameter 8 cm and height of 12 cm.

Here, diameter = 8 cm.

height = 12 cm.

Using the formula, V = ℼ(d/2)²h

V = 3.14159 × (8/2)² × 12 

= 3.14159 × 4² × 12 

= 3.14159 × 16 × 12

= 603.2
 

To find the volume of a cylinder with the slant height first, we need to find the height using the Pythagorean theorem, and then we use the formula, V = ℼr²h. 

For example, find the cylinder volume with a slant height of 13 cm and a radius of 5cm.

For finding the height using Pythagorean theorem, h = √l² - r²

= √13² - 5²

=  √169 - 25

=  √144

= 12

Now for finding the volume, V = ℼr²h

= 3.14159 × 5² × 12 

= 3.14159 × 25 × 12

= 942.48
 

The volume of the cylinder formula was derived by clearly understanding how much space the cylinder occupies. The volume of the cylinder can be calculated by using the volume formula. The following step-by-step explanation allows kids to understand how the formula is derived.

Step 1: Understanding shape 

The cylinder is like a stack of many discs placed on the top of the other. The volume of the cylinder is multiplied by the total area of the base with the height (number of discs stacked). 

Step 2: Find the area of the base

The base of a cylinder is circular. Therefore, the area of the circle is given as,

Area of base = ℼr².

Step 3: Multiplying the base with height

To get the total volume of cylinder, we need to multiply the area of base with height of the cylinder

Volume = Area of Base × Height.

V = ℼr² × h.

Step 4: Final Formula

The final formula is written as:

V = ℼr²h.
 

To find the volume of the cylinder, the following steps are used.

Step 1: Understanding the formula

The volume of a cylinder is: V = ℼr²h.

Here, V = volume of the cylinder

r = Radius of the base.

h = Height of the cylinder

ℼ is approximately 3.14

Step 2: Measuring the height and radius of the cylinder

Measure the radius of the base and the height of the cylinder.

Step 3: Use the formula

Apply the height and radius values and calculate, we will get the volume of a cylinder.
 

Understanding and learning the volume of a cylinder feels difficult for kids, but by using the tips and tricks below, kids can easily understand it. 

• Always remember the formula for the volume of a cylinder. Memorizing it makes the calculations easier.

• Use 3.14 for the value of ℼ, for simple calculations.

• Don’t do all the calculations in your head, write them step by step to avoid mistakes.

•  Volume - It is the amount of space inside a 3D shape. It tells how much something can contain or hold.

• Radius - It is the distance from the center of a circle to its edge.

• Cylinder - It is a 3D shape with two flat, circular bases and a curved size. It looks like a can or a tube.

• Pi - It is the special number used in math to calculate circles. It is approximately 3.14.