Lesson 5: The Volume of 3-D Objects
Explore 2
Cylinders
A cylinder is a prism with a circular base. Although you might not call a cylinder a circular prism, that’s exactly what a cylinder is.
Using the formula for the volume of a prism, what could be the formula for the volume of a cylinder?
Save your answer to your course folder (binder); then check in your textbook to see if your answer is correct. If it isn’t correct, what parts of your formula were correct? What parts of the formula need to be changed?
Here are a few examples to look over.
Example 1
Determine the volume of a soup can with a diameter of 3.5 in and a height of 4.5 in. Show your solution to the nearest tenth of a square inch.
Solution
Example 2
The volume of a cylinder is 200 cm3. Determine the radius of the cylinder to the nearest hundredth of a centimetre if the height of the cylinder is 8 cm.
Solution
Try This
Practice using the formula for the volume of a cylinder to solve these problems by completing them in your course folder ( binder).
Foundations and Pre-calculus Mathematics 10 (Pearson)
TT 1. Complete “Exercises” questions 6 and 18.c) on pages 42 and 43.
Use the link below to check your answers to Try This 1.
Cones
Math Lab: Volume of a Cone
Go to Math Lab: Volume of a Cone, print it (or copy by hand) and complete it.
Keep this in your course folder (binder) to refer to later.
Read
Go to your textbook to find the formulas for a cylinder and a cone and note how they are similar and how they are different. What fraction of the volume of a cylinder is the volume of a cone with the same height and radius?
Foundations and Pre-calculus Mathematics 10 (Pearson)
Read the top half of page 40. (You do not need to read “Example 3: Determining the Volume of a Cone” at this time. You will read it later in this lesson.)
Compare your experimental result in the cone investigation with the formulas you have just read in your textbook. Is your experimental result confirmed? Do your results support the finding that the volume of a cone is 
the volume of a cylinder with the same height and radius?
If your results do not support the ratio, give some reasons why you think this might be the case. Incorporate these comments into your Math Lab.
Read
Read your textbook again for “Example 3: Determining the Volume of a Cone” on page 40 and “Example 4: Determining an Unknown Measurement” on page 41 to see how the formula for the volume of a cone is applied. Use your calculator to verify the calculations. See the Caution bubble for a tip on using the calculator.
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Caution
When you use your calculator to evaluate a quotient, applying brackets in the right places can be the difference between getting a correct answer and a wrong one.
Say that you want to rearrange the formula for the volume of a cone to determine its height. Then 
becomes 
Evaluate the expression 
, where V = 20 cm3 and r = 2.5 cm.
After substituting, the expression would be 
.
Can you see what’s wrong with the following way of evaluating the expression?
(The solution, 119.4 cm, is much too large for a cone with a volume of only 20 cm3.)
By entering the keystrokes in this way, you would actually be evaluating
To evaluate the expression correctly, it is important to use brackets around the denominator:
The height of the cone is 3.06 cm. This answer is both reasonable and correct.
KEY IDEA
You have learned that the volume of a cone is the volume of a cylinder with the same radius and height. This ratio is the same for pyramids. In other words, the volume of a pyramid is the volume of the prism with the same height and base area.
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