221. Volume of Cylinders

Learning Intentions

• Apply the cylinder volume formula accurately.
• Substitute radius and height values into the formula.
• Solve cylinder volume problems in practical contexts.

Pre-requisite Summary

• A cylinder has two congruent, parallel circular bases.
• The height of a cylinder is the perpendicular distance between the circular bases.
• The area of a circle is found using .
• The volume of a cylinder is found using .
• The radius is half the diameter, so .
• Volume is measured in cubic units such as , and .
• Substitution means replacing pronumerals in a formula with given values.
• Practical volume problems require identifying the radius and height before calculating.

Worked Examples

Worked Example 1

Find the volume of a cylinder with radius and height .

Use:

Worked Example 2

Find the volume of a cylinder with radius and height .

Leave your answer in terms of .

Worked Example 3

A cylinder has diameter and height .

Find the volume.

Worked Example 4

A cylindrical water tank has radius and height .

Find the volume of water the tank can hold when full.

Worked Example 5

A cylindrical can has diameter and height .

Find the volume of the can.

Worked Example 6

A concrete pillar is shaped like a cylinder with radius and height .

Find the volume of concrete needed to make the pillar.

Problems

Problem 1

Find the volume of a cylinder with radius and height .

Use:

Problem 2

Find the volume of a cylinder with radius and height .

Leave your answer in terms of .

Problem 3

A cylinder has diameter and height .

Find the volume.

Problem 4

A cylindrical water tank has radius and height .

Find the volume of water the tank can hold when full.

Problem 5

A cylindrical can has diameter and height .

Find the volume of the can.

Problem 6

A concrete pillar is shaped like a cylinder with radius and height .

Find the volume of concrete needed to make the pillar.

Exercises

Understanding and Fluency

Exercise 1

Find the volume of a cylinder with radius and height .

Exercise 2

Find the volume of a cylinder with radius and height .

Exercise 3

Find the volume of a cylinder with radius and height .

Leave your answer in terms of .

Exercise 4

Find the volume of a cylinder with radius and height .

Leave your answer in terms of .

Exercise 5

A cylinder has diameter and height .

a) Find the radius.

b) Find the volume.

Exercise 6

A cylinder has diameter and height .

a) Find the radius.

b) Find the volume.

Exercise 7

A cylindrical container has radius and height .

a) Identify the radius.

b) Identify the height.

c) Find the volume.

Exercise 8

A cylindrical pipe has radius and length .

a) Identify the cylinder height.

b) Find the volume.

Exercise 9

Complete each substitution.

a) If and , then .

b) If and , then .

c) If and , then .

Exercise 10

Choose the correct cubic unit.

a) A cylinder measured in centimetres has volume in .

b) A cylinder measured in metres has volume in .

c) A cylinder measured in millimetres has volume in .

Reasoning

Exercise 11

Explain why the formula for the volume of a cylinder is:

Exercise 12

A student calculates the volume of a cylinder using:

Explain what is missing from the calculation.

Exercise 13

A cylinder has diameter .

A student substitutes into the volume formula.

Explain the error.

Exercise 14

Two cylinders have the same radius, but Cylinder A has twice the height of Cylinder B.

Explain how their volumes compare.

Problem-solving

Exercise 15

A cylindrical rainwater tank has radius and height .

a) Write the formula for the volume.

b) Substitute the radius and height.

c) Find the volume of the tank.

Exercise 16

A candle is shaped like a cylinder with diameter and height .

a) Find the radius.

b) Find the volume of wax needed.

c) State the answer using cubic units.

Exercise 17

A cylindrical glass has radius and height .

a) Find the volume.

b) Explain what the volume represents in this context.

c) State whether the answer should use square units or cubic units.

Exercise 18

A cylindrical concrete post has diameter and height .

a) Find the radius.

b) Find the volume of concrete required.

c) Explain why the height must be the perpendicular distance between the circular bases.

Potential Misunderstandings

• Confusing radius and diameter.
• Substituting the diameter into instead of the radius.
• Forgetting to square the radius before multiplying by height.
• Writing instead of .
• Using square units instead of cubic units for volume.
• Thinking the height of a cylinder is the circumference of the circular base.
• Forgetting that the circular base area is .
• Rounding too early when using .
• Assuming volume measures the outside surface instead of the space inside the cylinder.

Next: 222. Total Surface Area of Right Prisms