The volume of a cylinder helps us understand how much three-dimensional space is present inside a cylindrical object. Whether it’s a water bottle, a tank, a pipe, or even a measuring container, this formula tells us how much capacity it can hold. In mathematics and real-world applications, knowing how to calculate the volume of a cylinder is important for storage, construction, engineering, and competitive exams. The formula is simple and widely used across various fields.
Volume of a Cylinder Formula Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| V = πr²h | r = radius, h = height, π = 3.1416 | Used to find the total capacity inside a cylinder |
What is Volume of a Cylinder in Maths?
In mathematics, the volume of a cylinder represents the total amount of space enclosed inside it. It is measured in cubic units such as cm³, m³, or liters. The formula is derived by multiplying the area of the circular base (πr²) by the height (h) of the cylinder.
A cylinder has two equal circular bases and a fixed height connecting them. The volume tells how much liquid, gas, or material can fit inside the cylinder. To calculate it, simply multiply:
Volume = π × r² × h
This formula is widely used in daily life, such as calculating the water capacity of a bottle, tank, pipe, or cylindrical container. It is also an important topic for exams like CUET, SSC, Banking, and JEE, where mensuration questions frequently appear.
Examples to Calculate Volume of a Cylinder
Example 1: Radius = 7 cm, Height = 10 cm
Step 1: V = πr²h
Step 2: = 3.14 × 7² × 10
Step 3: = 3.14 × 49 × 10 = 1538.6 cm³
So, the volume of the cylinder is 1538.6 cm³.
Example 2: Radius = 5 m, Height = 20 m
Step 1: Volume = πr²h
Step 2: = 3.14 × 5² × 20
Step 3: = 3.14 × 25 × 20 = 1570 m³
So, the volume of the cylinder is 1570 m³.
FAQs about Volume of a Cylinder Formula
Q1. What is the volume of a cylinder?
It is the total space a cylinder occupies, measured in cubic units.
Q2. What is the unit of cylinder volume?
Volume is measured in cm³, m³, mm³, or liters depending on the size.
Q3. What is the formula for volume of a cylinder?
The formula is V = πr²h, where r is radius and h is height.
Q4. What does π represent in this formula?
π is a constant value (3.1416) used in all circle-related calculations.
Q5. Where is this formula used in practical life?
It’s used to measure capacities of water tanks, pipes, cans, bottles, and cylinders.
Q6. How can the volume of a cylinder be increased?
By increasing the radius, the height, or both.