How to Find the Volume of Solids - The Basics

Lesson Objective

This lesson is an introduction to the basic ideas on how to find the volume of solids. We will be using a rectangular solid and a cylinder as examples.

About This Lesson

After familiarizing with surface area, it is time to learn about the volume of solids. As an introduction, we will be learning on how to find the volume of the following solids:

Rectangular Solid
Cylinder

This lesson also emphasizes on getting the unit for volume correctly.

The study tips and math video below will explain more.

Study Tips

Tip #1 - Rectangular Solid

To find the volume (V) of a rectangular solid, we just need to multiply the width (W), length (L) and height (H) of the solid together as shown below:

V = WLH

rectangular solid with width R, length L and height H

The math video below will explain this further...

Tip #2 - Cylinder

Now, to find the volume (V) of a cylinder, you just need to multiply the area of the base (πR²) with the height (H) together. This formula is shown below:

V = πR²H

The symbol, π, is just a number that is approximately equals to ²²/₇ or 3.142.

The math video below will explain this further...

Tip #3 - Unit for Volume

It is important to get the unit for volume correctly. Here are some pointers:

First, make sure all the units are the same
Let's say that the width, length and height of a rectangular solid are given as follow:

Width (W)	= 20mm
Length (L)	= 5cm
Height (H)	= 3cm

Width (W)	= 2cm
Length (L)	= 5cm
Height (H)	= 3cm

Next, understand what unit³ (cubic unit) means
Now, after ensuring the units are the same, we can calculate the volume, V below:
V = WLH
= 2×5×3
= 30 cm³
Notice the cm³ (cubic centimeter) above? This 'cubic' comes about because we multiplied 3 lengths that are in cm. If W, L and H are in feet (ft), the unit for volume will be ft³ (cubic feet). Generally speaking, unit³ is the unit for volume where the unit can be mm, cm, m, feet, km, miles etc.

The math video below will explain this further...

Math Video

Lesson Video

Math Video Transcript

00:00:03.200
In this lesson, we will learn the basics ideas on how to find the volume of solid.

00:00:09.080
To explain the basics, we will be using a rectangular solid, and a cylinder as examples.

00:00:16.080
Now, consider this rectangle with a width of W centimeter, and the length of L centimeter.

00:00:23.020
By now, we should know that the Area A, of this rectangle is W multiply L.  

00:00:30.070
Since we are multiplying 2 lengths with unit centimeter, the unit for the area will be  square centimeter.

00:00:37.090
Hence, the area of this rectangle is WL square centimeter.

00:00:43.220
Next, let's change this rectangle into a rectangular solid. Observe that, this rectangular solid now have a width of W centimeter, length of L centimeter, and the height of H centimeter.

00:00:58.170
Notice that, this solid is occupying certain amount of space, and the amount of space occupied is called Volume, V.

00:01:07.110
Now, how to find the volume of this rectangular solid? We just need to multiply the area. A, with the height, H.

00:01:17.000
Hence, by multiplying W, L and H, we get the volume of this rectangular solid as WLH.

00:01:26.080
Now, this volume WLH will only makes sense, if we include the unit for it.

00:01:32.140
Here's how. Since we are multiplying these 3 lengths with the unit centimeter together, the unit for this volume will be cubic centimeter.

00:01:41.240
Hence, the volume of this rectangular solid will be WLH cubic cm.

00:01:51.230
Next, let's learn on how to find the volume of a cylinder.

00:01:55.210
Consider this circle, with the radius R inches.

00:02:00.130
By now, we should know that the Area, A of this circle is PI r square.

00:02:06.100
Since the radius is in inches, the unit for the area of this circle will be square inch. 

00:02:12.150
Hence, the area of this circle is pi r square, square inch.

00:02:19.190
Now, let's change the circle into a cylinder.

00:02:24.010
After doing so, this cylinder has the radius of R inches, and the height of H inches.

00:02:31.120
Notice that, this cylinder occupies certain amount of space. The amount of space occupied is the volume, V.

00:02:40.180
How to find the volume of this cylinder? To do so, we just need to multiply the area, A with the height, H. Hence, multiplying pi R square with H gives, pi R square H.

00:02:54.140
Now, this pi R square H only makes sense, if we include the unit for it. 

00:03:00.160
Here's how. Since we are multiplying R square with H, notice that, this is actually multiplying 3 lengths with the unit inch together.

00:03:10.080
This will give the unit for this volume as, cubic inch.

00:03:15.140
Hence, the volume this cylinder will be πR2H cubic in.

00:03:21.110
That is all for this lesson. Try out the practice question to further your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on how to find the volume of solids or pick your choice of question below.

Question 1 on how to find the volume of a rectangular solid
Question 2 on how to find the volume of a cylinder

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