Contents

**Capacity|Definition & Meaning**

**Definition**

Calculating **how much** **fluid** can f**it inside** a **container** is called **capacity** in mathematics. Similarly, **every object** is **limited** to the **maximum** **amount** of **water** it can **hold**, just as glass can only hold a certain amount. Our everyday lives are filled with **hollow objects**, as we know so the maximum **amount of matter** an **object** can have can be defined as **capacity**. Usually, capacity can be **measured** in **liters, milliliters, gallons**, etc.

Air or liquid is **filled** within **hollow objects,** giving the containers their shape. In a container, its **capacity** is **determined** by the **amount of air** and **water accumulated** inside. Although there are many similarities between volume and capacity, we can still distinguish between them. The **capacit**y of a container **refers** to the amount of **solid, liquid, or gas** it can contain, as well as its weight.

**Illustration of Capacity**

Above, we can see that the **jar** is **partially filled** with water. The **capacity** of the jar indicates the **amount of water** it can **hold.** Alternatively, the formula of the volume of a jar /cylinder can be used to find the jar’s capacity.

In the figure shown above, we can see a square **water tub** whose capacity might be around **4 to 5 liters**.

The above figure shows the **various objects** having capacity, in the **cup**, there is generally a **capacity** of **250mL to 500ml**, the capacity of a **cone** varies from application to application but its generally around **30mL** and the capacity of the **cylinder** can also be calculated by the dimensions of the cylinder, it usually ranges around **5L**.

**Units of Capacity**

The **standard unit** for capacity is **Litre or milliliter** but other than that also various units for capacity used in daily life include **gallon, quart, and a pint**. We will discuss them one by one.

**Litre**

** **The liter is a **metric measurement unit** that measures **volume and capacity**. **Containers** are **measured** by their **capacity**, **not** their **volumes.** Volume denotes how much **space** a** liquid occupies**, while **capacity** indicates how much liquid can be **contained**.

**Milliliter**

** **Using milliliters as **measurements of liquid** capacity, the metric system has been simplified. Liquids of a **smaller** volume or **capacity**, such as **pharmaceutical solutions**, are measured with this unit. In **metric systems**, milliliters are** abbreviated** **mL.**

**Gallon**

** ****U.S. customary and imperial systems** of measurement define the gallon as a **unit** of volume and **capacity**.

**Pint**

It is also a **unit of capacity** and it is equal to around **0.47 liter**.

**Quart**

** **It is equal to **Â¼ of a gallon** or **two pints** or **0.94 liter**

**Conversion Between Units**

**1 Litre** = 1000ml

**1 mL** = 1/1000L

**1 Gallon** = 3.785L

**1 pint =** 0.473L

**1 Quart** = 0.94L

**Capacity and Volume Comparison**

There are several **differences** between **capacity and volume** that make the two terms different, but **usually,** they are **treated** as the** same**. **Volume** refers to the **area o**f a **particular space** containing a total amount of any substance contained within it. An area’s** capacity** refers to its **ability** **to contain** all of the **substances** that it can **hold**.

For **volume**, we have the following facts:

- Objects in
**three dimensions**are measured by their**volume,**which represents their**coverage of space**. - The unit to express volume is a
**meter cube**or**centimeter cube.** - The
**objects**that have**volume**are usually**in form**of**solids**like**ice,**and**hollow**like hollow**cones.**

Whereas, for **capacity**, we have:

- Objects are
**capable**of**holding**,**absorbing**, or**receiving**something that has the capacity (such as solids, gases, or liquids). - Units to express capacity include
**Litre, milliliter**, gallon, pint, quart, etc. **Only hollow objects**have capacity like**cones**and**cylinders.**

Thus, the two terms mean different things, although they are closely related.

**Examples of Calculating Capacities**

**Example 1**

Consider a cube **water tub** and the **capacity** of the object is **1.75 Litres** **convert** the capacity into (a) milliliter (b) Gallon (c) Pint (d) Quart.

**Solution**

**(a) Litre to mL:**

1 Litre = 1000ml

1.75 Litre = 1000 x 1.75 Litre

**1.75 Litre = 1750mL**

**(b) Litre to Gallon (US):**

3.785 L = 1 Gallon

1 Litre = 0.2641 Gallon

1.75 Litre = 0.2641 x 1.75 Litre

**1.75 Litre = 0.462175 Gallon**

**(c) Litre to Pint**

0.473L = 1 pint

1 Litre = 2.113 pint

1.75 Litre = 2.113 pint x 1.75 Litre

**1.75 Litre = 3.698 pint**

**(d) Litre to Quart**

0.956L = 1 Quart

1 Litre = 1.056 Quart

1.75 Litre = 1.75 Litre x 1.056 Quart

**1.75 Litre = 1.849 Quart**

**Example 2**

Consider the **two aquariums** labeled aquarium 1 and aquarium 2. There is a **bucket** of **capacity** having **1 Litre.** How will you **measure** the **capacity** of **aquarium 1** and **aquarium 2** from the bucket? Explain the hypothetical procedure.

**Solution**

First, let us find the** capacity of Aquarium 1.**

We are given a **bucket** having a **1 litre capacity** so we will do a small **activity**. First, we will **fill** the **bucket** with **water** and **pour** the bucket **until** the **aquarium** is **full.** So when we kept on pouring the water from the bucket into the aquarium we came to know that **it takes 5 buckets** to **fill** the **whole aquarium** 1 so mathematically.

1 bucket = 1 litre

No of bucket poured to fill the aquarium 1 to full = 5 = Capacity of Aquarium

Capacity of Aquarium 1 = 5 buckets x 1 litre

**Capacity of Aquarium 1 = 5 Litres**

Now, let us find the** capacity of Aquarium 2.**

On repeating the above methodology or when we kept on **pouring** the **water** from the **bucket** into **aquarium 2** we came to know that **it takes 10 buckets** to fill the whole **aquarium 2** so mathematically.

1 bucket = 1 litre

No of buckets poured to fill the aquarium 2 to full = 10 = Capacity of Aquarium

Capacity of Aquarium 2 = 10 buckets x 1 litre

**The capacity of Aquarium 2 = 10 Litres**

**Example 3**

Consider a **Flask and spoon**. The **capacity** of the **spoon** is **10mL** and we want to **find **the **capacity** of the **Flask.** Explain the hypothetical procedure.

**Solution**

We have a **spoon** of **10mL** and a **flask** with an **unknown** **capacity** so what we will do is we will keep on **adding liquid** **in** a 10mL **spoon** and **pour** it into the **flask**, we will **continue** to perform the activity **unless** the **flask** reaches a **full quantity.** Let’s **suppose** we put **20 spoons** full of liquid into the **flask** so that it **reached** its **full quantity** so mathematically.

1 spoon = 10mL

No of spoon poured to fill the flask = 20

The capacity of the flask = capacity of spoon * no of spoon poured to fill the flask

Capacity of flask = 10ml x 20

**Capacity of flask = 200ml**

*All mathematical drawings and images were created with GeoGebra.*