Prisms & cylinders · Ages 13–14
Volume of a cylinder
V = πr²h; halve a diameter first.
How to do it
Method
V = πr²h; halve a diameter first
r = 3, h = 10: 9π × 10 = 90π cm³
Another way
π in at the end
90π ≈ 90 × 3.14 = 282.6
In full
A cylinder is a prism too: volume = base area × height = πr²h, r the base's radius. Find the base area πr² first, then multiply by the height. Radius 3 cm, height 10 cm: base area π × 32 = 9π cm², volume 9π × 10 = 90π cm³. The answer can keep the π (in terms of π), or put a value of π in at the very end: taking π as 3.14, 90π = 90 × 3.14 = 282.6 cm³. Keeping π to the last step keeps the numbers simple and stops rounding piling up. Careful: given the diameter, halve it for the radius; r² is r × r, not 2r. The other way round, from the volume: h = V ÷ (πr²); for the radius, r² = V ÷ (πh), then take the square root.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The cylinder in the picture has a base 4 cm across and a height of 16 cm. What is its volume, in terms of π?
Show the answer and working
Answer: 64 π cm³
The radius is half the diameter, 4 ÷ 2 = 2 cm; volume π × 22 × 16 = 64π cm³.
Example 2
The cylinder in the picture has a base radius of 2 cm and a height of 17 cm. What is its volume, in terms of π?
Show the answer and working
Answer: 68 π cm³
Base area π × 22 = 4π cm², volume = base area × height = 4π × 17 = 68π cm³.
Example 3
The cylinder in the picture is 10 cm across and 4 cm high. What is its volume?
- A. 100π cm³
- B. 20π cm³
- C. 40π cm³
- D. 400π cm³
Choose the right answer
Show the answer and working
Answer: A. 100π cm³
The radius is 10 ÷ 2 = 5 cm, so the volume is π × 52 × 4 = 100π cm³.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The cylinder in the picture is 16 cm across and 19 cm high. What is its volume?
- A. 4864π cm³
- B. 304π cm³
- C. 1216π cm³
- D. 152π cm³
Choose the right answer
Answer:
2.The cylinder in the picture has a base radius of 5 cm and a height of 2 cm. What is its volume, in terms of π?
Answer:
3.The cylinder in the picture has a base 20 cm across and a height of 9 cm. What is its volume, in terms of π?
Answer:
4.A cylinder 10 cm across and 20 cm high has a volume of 200π cm³.
True or false?
Answer:
5.The cylinder in the picture has a volume of 225π cm³ and a height of 9 cm. What is its base radius r, in cm?
Answer:
All the answers
- 1. C. 1216π cm³
- 2. 50 π cm³
- 3. 900 π cm³
- 4. False
- 5. 5 cm
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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