Volume of Prisms and Cylinders
The universal volume formula $V = A_{base} \times h$ applies to every prism. Extend it to cylinders and convert between volume and capacity.
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Worksheet
Download or print the worksheet to work through this lesson.
Q1: A fish tank measures 60 cm by 30 cm by 40 cm. Estimate its capacity in litres without doing any exact calculations. (Hint: think about what fits in a 1-litre milk carton.)
Q2: Two cylinders have the same height. Cylinder A has radius 4 cm and Cylinder B has radius 8 cm. Without calculating, how many times larger do you think Cylinder B's volume is? Explain.
Learning Intentions
Know
- The universal prism volume formula $V = A_{base} \times h$.
- The cylinder volume formula $V = \pi r^2 h$.
Understand
- That a cylinder is a prism with a circular base.
- How to convert between cm$^3$, m$^3$, litres and millilitres.
Can Do
- Calculate the volume of any right prism and cylinder.
- Convert between volume and capacity units.
Success Criteria
- I can calculate the volume of a rectangular prism, triangular prism and cylinder.
- I can convert between cubic centimetres, cubic metres, litres and millilitres.
- I can solve word problems involving volume and capacity in context.
Key Terms
Common Mistakes to Avoid
Wrong: Using the slant height instead of the perpendicular height when calculating the volume of a prism with a triangular base.
Right: Volume always uses the perpendicular height of the prism, not the slant height of the base triangle.
Wrong: Confusing 1 m$^3$ = 1000 L with 1 cm$^3$ = 1 mL. The conversions are different scales.
Right: 1 cm$^3$ = 1 mL. 1 m$^3$ = 1000 L = 1,000,000 cm$^3$.
Every prism has the same volume formula: find the area of the base, then multiply by the height (the perpendicular distance between the two bases).
For a rectangular prism: $V = l \times w \times h$
For a triangular prism: $V = \left(\frac{1}{2} \times b \times h_{triangle}\right) \times h_{prism}$
For a cylinder: $V = \pi r^2 \times h$
Unit conversions: $1$ cm$^3$ = $1$ mL. $1000$ cm$^3$ = $1$ L. $1$ m$^3$ = $1000$ L. Always check your final answer uses the units asked for.
What to write in your book
- Universal prism formula: $V = A_{base} \times h$
- Rectangular prism: $V = lwh$
- Triangular prism: $V = (\frac{1}{2}bh) \times L$
- Always use perpendicular height, not slant height
Correct! $V = 6 \times 5 \times 4 = 120$ cm$^3$.
Not quite. $V = 6 \times 5 \times 4 = 120$ cm$^3$.
A cylinder is simply a prism with a circular base. The same universal formula applies.
Remember: if you are given the diameter, divide by 2 to get the radius before substituting.
What to write in your book
- Cylinder: $V = \pi r^2 h$
- If given diameter, divide by 2 to get radius first
- A cylinder is a prism with a circular base
Correct! $V = \pi r^2 h = \pi(3)^2(7) = 63\pi$ cm$^3$.
Not quite. $V = \pi r^2 h = \pi(3)^2(7) = 63\pi$ cm$^3$.
Interactive: Volume Comparator
Your Turn
Question 1: Find the volume of a rectangular prism with dimensions 15 cm by 10 cm by 8 cm, in litres.
Question 2: A cylinder has radius 5 cm and height 12 cm. Find its volume in cm$^3$.
Question 3: A swimming pool is 25 m by 10 m with an average depth of 1.8 m. How many kilolitres of water does it contain?
Revisit Your Thinking
Look back at your Think First answer about the fish tank. Calculate the exact volume in litres. The tank is only filled to 40 cm deep. How many litres does it now contain? What percentage of the total capacity is this?
Earlier you were asked: What was your first thought on this topic?
Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?
What is the volume of a rectangular prism with dimensions 6 cm, 5 cm and 4 cm?
A cylinder has radius 3 cm and height 7 cm. What is its volume?
How many litres are in 2500 cm$^3$?
A triangular prism has a base triangle with base 10 cm and height 6 cm. The prism length is 15 cm. What is its volume?
Which solid has the greatest volume: a cube of side 6 cm, or a cylinder of radius 4 cm and height 6 cm?
A cylindrical rainwater tank has diameter 2.4 m and height 2.5 m.
(a) Find the volume of the tank in m$^3$. (2 marks)
(b) Convert this volume to kilolitres. (1 mark)
A rectangular aquarium measures 90 cm by 45 cm by 50 cm.
(a) Find its total capacity in litres. (2 marks)
(b) The aquarium is filled to 4 cm from the top. How many litres of water does it contain? (2 marks)
A concrete path 1.2 m wide is laid around a rectangular garden bed measuring 8 m by 5 m. The concrete is 10 cm thick.
(a) Find the outer dimensions of the concrete path. (1 mark)
(b) Find the area of the concrete path (as a composite shape). (2 marks)
(c) Find the volume of concrete needed, in m$^3$. (1 mark)
(d) If concrete costs $\$180$ per m$^3$, calculate the total cost. (1 mark)
Prism
$V = A_{base} \times h$
Rectangular
$V = lwh$
Triangular
$V = \frac{1}{2}bh \times L$
Cylinder
$V = \pi r^2 h$
1 cm$^3$
= 1 mL
1 m$^3$
= 1000 L
Real-Life Link
Australian households use volume calculations daily. A standard bathtub holds about 150 litres. A 10-minute shower with a water-efficient head uses about 90 litres. Sydney's Warragamba Dam has a capacity of about 2,027,000 megalitres — enough to supply Greater Sydney for years. Farmers in drought-prone regions calculate tank volumes carefully: a 22,500-litre poly tank (common in rural Australia) has diameter about 3.6 m and height about 2.2 m. Understanding these calculations helps Australians manage water use during restrictions and droughts.
Game Time!
Test your volume skills in an interactive challenge.
Play Volume Challenge