Volume

When you connect one point to another point, you get a line segment.

A **line segment**** **is **one-dimensional**. It is **measured by ****length only**.

These shapes are two-dimensional.

They are flat and only have **two dimensions**. These dimensions are **width and height**.

They are **measured by area**.

The world we live in is **three-dimensional**.

The objects that we encounter every day are like these:

They are **solid**. This means that they have three dimensions which are **width, height, and depth**.

**3-dimensional objects **are **measured by their volume**.

When we measure the **area **of a flat shape, we think of it as the space that it occupies.

Let's say we have this rectangle.

We count the square units that it covers.

This rectangle covers 12 squares.

Since each square unit is 1 square meter, the area of this rectangle is 12 square units.

It can also be written as 12 m².

Other units of area are square centimeters (cm²), square inches (in²), square feet (ft²), square miles (mi²), and even square kilometers (km²).

**Volume **is the amount of space that a solid object takes up.

Finding the volume of a 3-D shape is similar to finding the area of 2-D shapes - but only with 1 additional dimension to include.

Take a look at this cube. It has 3 dimensions.

To know its **volume**, we figure out **how many ****cubic units**** can fit in it**.

Cubic units are almost like square units, but they **have depth**.

The volume of this object 👆 is** 16 cubic units.**

A **cubic unit **is 1 unit high, 1 unit wide, 1 unit deep.

**Tip:**** Cubic **sounds like **cube**. They mean almost the same thing.

Since counting cubic units takes quite a long time to do, we can just use a formula to find the **volume of a cube**:

volume =widthxheightxdepth

It doesn't matter which numbers you multiply first, you'll still get the same answer.

😃 The important thing is to** multiply all three**.

Let's figure out the volume of this cube.

We see three lengths measured in meters.

Let's multiply them to find the volume in cubic meters.

6x6x6=?

Start by multiplying the first two numbers.

6x6=36

Now, we multiply the product we got with the last number.

36x6=216

The volume of this cube is **216 cubic meters**.

We write **cubic meters **after the number because we've multiplied the lengths in meters three times.

We can also write cubic meters as **m³**. It's read as "cubic meter*".*

So we can also say that the volume is **216 m³ **(it is read as 216 cubic meters).

Other **units of volume **are cubic centimeters (cm³), cubic inches (in³), cubic feet (ft³), cubic miles (mi³), and cubic kilometers (km³).

Take a look at this box.

We see that it has a width, height, and depth. 👆

To find its volume, we multiply the three dimensions.

volume =3 ftx5 ftx2 ft

Start by multiplying the first two numbers.

3x5=15

Then, multiply the product you got by the last length.

15x2=30

The final product is 30.

The dimensions of the box was measured in inches.

So the unit of volume we write after the number is cubic inches or inches cubed (in^{3}).

✅ The volume of this box is **30 cubic inches **or **30 in³**.

Great work!

Now, you can move on to practice. 👏

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