# How to Find Volume? – Formula and Examples

#### Table of Contents

## Introduction

**Volume**

In geometry, the concept of volume plays a crucial role in determining the amount of space occupied by a three-dimensional object. Whether it’s a simple cube or a complex cylinder, understanding how to find the volume of various shapes is essential for solving mathematical problems and real-world applications.

## Analogy of Definition

**What is Volume?**

Volume refers to the amount of space occupied by a three-dimensional object. It is measured in cubic units, such as cubic centimetres or cubic meters. The volume of an object can be calculated by determining the total amount of space it encloses.

## Method

**How to Find Volume?**

The method for finding the volume of different shapes varies based on their unique properties. For example, the volume of a cube can be found by simply cubing the length of one of its sides, while the volume of a cylinder requires the use of its base area and height. Understanding the specific formulas and techniques for each shape is essential for accurate volume calculations.

**Volume of 3 Dimensional Shapes**

**Volume of a Cylinder**

The volume (V) of a cylinder can be calculated using the formula:

** V = πr ^{2}h**

Where,

V = Volume

π = Pi (approximately 3.14159)

r = Radius of the base

h = Height of the cylinder

** Volume of a Rectangular Prism / Cuboid**

The volume (V) of a rectangular prism can be calculated using the formula:

** V = l * w * h**

Where,

V = Volume

l = Length

w = Width

h = Height

** Volume of Sphere**

The volume (V) of a sphere can be calculated using the formula:

** V = (4/3)πr ^{3}**

Where:

V = Volume

π = Pi (approximately 3.14159)

r = Radius of the sphere

**Volume of Cube**

The volume (V) of a cube can be calculated using the formula:

** V = s ^{3}**

Where:

V = Volume

s = Length of one side of the cube

**Volume of Cone**

The volume (V) of a cone can be calculated using the formula:

** V = (1/3)πr ^{2}h**

Where:

V = Volume

π = Pi (approximately 3.14159)

r = Radius of the base

h = Height of the cone

**Volume Formulas**

Learn about volume in a fun and interactive way, visit our site ChimpVine.

## Examples

**Finding the Volume of Different Shapes**

**Example 1: Finding the Volume of a Cylinder**

Given: Radius (r) = 5 cm, Height (h) = 10 cm

Using the formula V = πr^{2}h

V = π * (5cm)^{2} * 10 cm

V ≈ 785.4 cm^{3}

**Example 2: Finding the Volume of a Rectangular Prism**

Given: Length (l) = 6 cm, Width (w) = 4 cm, Height (h) = 3 cm

Using the formula V = l * w * h

V = (6 x 4 x 3) cm

V = 72 cm^{3}

**Example 3: Finding the Volume of a Sphere**

Given: Radius (r) = 3 cm

Using the formula V = (4/3)πr^{3}

V = (4/3) * π * (3 cm)^{3}

V ≈113.1 cm^{3}

**Example 4: Finding the Volume of a Cube**

Given: Length of side (s) = 5 cm

Using the formula V = s^{3}

V = (5 cm)^{3}

V = 125 cm^{3}

**Example 5: Finding the Volume of a Cone**

Given: Radius (r) = 4 cm, Height (h) = 8 cm

Using the formula V = (1/3)πr^{2}h

V = (1/3) * π * (4 cm)^{2} * (8 cm)

V ≈ 134.04 cm ^{3}

## Quiz

## Tips and Tricks

**1. The Cylinder Challenge**

**Tip: **Use the formula V = πr^{2}h to calculate the volume of a cylinder. If the radius and height of a cone is equal, then its volume will be 1/3 th the volume of cylinder.

**2. The Rectangular Prism Puzzle**

**Tip: **Use the formula V = l * w * h to find the volume of a rectangular prism. Rectangular prism is also known to be a cuboid.

**3. The Sphere Quest**

**Tip: **Use the formula V = (4/3)πr^{3} to calculate the volume of a sphere.

**4. The Cube Conundrum**

**Tip: Use the formula V = s ^{3} to determine the volume of a cube.**

**5. The Cone Challenge**

**Tip: Use the formula V = (1/3)πr ^{2}h to find the volume of a cone.**

## Real life application

**Story: “The Volume Adventures of Maya and Ethan”**

Maya and Ethan, two young explorers, embarked on a series of adventures that required them to apply their knowledge of volume to overcome challenges and solve mysteries.

**Challenge 1: The Treasure Chamber**

Maya and Ethan discovered an ancient treasure chamber filled with various geometric artifacts. To unlock the chamber, they needed to calculate the volume of a cylindrical container that held precious gems. Using the formula V = πr^{2}h they determined the volume and gained access to the treasure.

**Challenge 2: The Enchanted Forest**

As they ventured into an enchanted forest, Maya and Ethan encountered a magical sphere that emitted a mysterious glow. To understand its significance, they calculated the volume of the sphere using the formula V = (4/3)πr^{3}. The volume revealed the sphere’s hidden power, guiding them on their quest.

**Challenge 3: The Secret Temple**

In their final challenge, Maya and Ethan entered a secret temple where they encountered a massive rectangular prism that concealed a legendary artifact. By calculating the volume of the prism using the formula V = lwh, they unveiled the artifact and completed their extraordinary journey.

## FAQ's

^{2}) and height (h), while other shapes have unique formulas based on their specific dimensions and properties. Understanding the distinct formulas for each shape is essential for accurate volume calculations.

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