Volume and Capacity

In Class 4 Maths, we learn about many interesting concepts and “Volume and Capacity” is one such topic. This topic helps us understand how much space an object occupies, and how much fluid it contains, be it water, juice or any other liquid. Understanding volume and capacity is important in our daily lives, as it is involved in cooking, filling gas in the car, and even packing for a trip!

Understanding volume

Volume refers to the amount of space an object occupies. Imagine you have a box full of chocolates. To know how many chocolates it can hold, you need to know the volume of the box. It is like measuring how much space is inside the box.

In mathematical terms, volume is usually measured in cubic units. A cubic unit can be a cubic centimeter (cm 3), cubic meter (m 3), or cubic inch (in 3), depending on the size of the object you're measuring.

Example of cubes

Imagine a small cube that measures 1 centimeter on all sides. This is called a cubic centimeter. This small cube helps us imagine how we can measure the space inside larger shapes with the same small cube.

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/ |    /  | 
+------+   |
|      |   +
|      +---+ | 
|      /   | 
|/     |/  
+------+

Calculating volume

To find the volume of a cube or rectangular prism we can use this simple formula:

Volume = Length × Width × Height

Example

Let's consider a box with the following dimensions: length = 4 cm, width = 3 cm, and height = 2 cm. What is the volume of the box?

Using the formula, we get:

Volume = 4 cm × 3 cm × 2 cm = 24 cm 3

This means the volume of the box is 24 cubic centimeters.

Introduction to capacity

Capacity is a term that is closely related to volume, but it specifically refers to how much liquid a container can hold. For example, when we fill a water bottle, we are concerned about the capacity of the bottle.

Units of capacity

Capacity is usually measured in liters (L) or milliliters (mL). Now, you might be wondering what is the difference between liters and milliliters? Well, 1 liter is equal to 1,000 milliliters. Here is the relation:

1 Liter = 1,000 Milliliters

Example

Consider a water bottle that can hold 500 mL of water. If you have two such bottles, the total capacity will be 1,000 mL, which is equal to 1 liter.

Adding volume and capacity

Although volume and capacity are about space, they are used slightly differently. Volume typically refers to how much space an object or shape takes up in units such as cubic centimeters. Capacity focuses on the amount of liquid a container can hold, often in liters or milliliters.

Sometimes, you may have a container where you are asked for both volume and capacity. Consider a rectangular tank:

Volume and capacity of the tank

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/              /| 
/              / | 
+---------------+  | 
|      |       |   +
|      +-------|---+
|      /       |
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+---------------+
Length = 5 m
Width = 3 m
Height = 2 m

To find the volume of the tank we use the formula:

Volume = Length × Width × Height = 5 m × 3 m × 2 m = 30 m 3

This means that the volume of the tank is 30 cubic meters.

Thinking about its water holding capacity, if 1 cubic meter can hold 1,000 liters of water, then the tank can hold the following:

Capacity = Volume in m 3 × 1,000 L/m 3 = 30 × 1,000 = 30,000 L

30,000 litres of water can be filled in this tank.

Real-life examples

Here are a few more scenarios to help you better understand volume and capacity:

1. Swimming pool

Suppose you have a rectangular swimming pool 10 m long, 5 m wide and 2 m deep. To find out how much water the pool can hold, we first calculate the volume, then convert it to capacity.

Volume = Length × Width × Height = 10 m × 5 m × 2 m = 100 m 3 
Capacity = Volume in m 3 × 1,000 L/m 3 = 100 × 1,000 = 100,000 L

The swimming pool can hold 100,000 litres of water.

2. Measuring cup

If you have a measuring cup with a maximum capacity of 250ml, this means it can hold 250ml of liquid, such as water, milk or juice.

3. Gas tank

Consider a car whose fuel tank has a capacity of 50 liters. If you fill the tank to the top, it will contain 50 liters of gasoline or fuel.

Practice problems

Let's practice what we've learned. Try solving these problems yourself:

Problem 1

A grain box has a length of 30 cm, a width of 10 cm and a height of 20 cm. What is the volume of the grain box in cubic centimeters?

Problem 2

A rectangular fish tank is 120 cm long, 40 cm wide and 30 cm high. Calculate its volume and determine its capacity in liters, knowing that 1,000 cm ³ is equal to 1 liter.

Problem 3

A milk jug can hold 2 liters of milk. How many milliliters of milk can the jug hold?

Solution:

Try to troubleshoot the problems above before looking at these solutions!

Solution to Problem 1

Volume = length × breadth × height = 30 cm × 10 cm × 20 cm = 6,000 cm ³

Solution to Problem 2

Volume = length × breadth × height = 120 cm × 40 cm × 30 cm = 144,000 cm ³

Capacity = Volume in cm ³ ÷ 1,000 = 144,000 ÷ 1,000 = 144 litres

Solution to Problem 3

Since 1 liter = 1,000 milliliters, 2 liters = 2 × 1,000 = 2,000 milliliters

Conclusion

Both volume and capacity are important concepts not only in math but also in real-world applications. Remember that they are related but still serve different purposes. Volume helps us understand the space taken up by objects, while capacity tells us how much fluid a container can hold.

By practicing and using real-life examples, you can become more familiar with these concepts. Whether planning a party, going shopping, or doing a science experiment, understanding volume and capacity will definitely help you make better decisions. Keep practicing, and soon you'll be a pro at measuring spaces and capacities!

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