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
The π key at the end
90π ≈ 283 (3 sig. fig.)
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); where a number is wanted, press the calculator's π key at the very last step and round as the question asks, to 3 significant figures if it doesn't say: 90π ≈ 282.74…, so 283 cm³. Not 3.14 or 227: the answer stays accurate. 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 volume of 108π cm³ and a base radius of 6 cm. How high is it, in cm?
Show the answer and working
Answer: 3 cm
The base area is π × 62 = 36π cm², so the height = volume ÷ base area = 108π ÷ 36π = 3 cm.
Example 2
A cylinder 4 cm across and 14 cm high has a volume of 56π cm³.
True or false?
Show the answer and working
Answer: True
The radius is 2 cm, so the volume is π × 22 × 14 = 56π cm³.
Example 3
The cylinder in the picture has a volume of 405π cm³ and a height of 5 cm. What is its base radius r, in cm?
Show the answer and working
Answer: 9 cm
πr² × 5 = 405π, so r² = 405 ÷ 5 = 81 and r = 9 cm (9 × 9 = 81).
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 has a base radius of 10 cm and a height of 10 cm. What is its volume, in terms of π?
Answer:
2.The cylinder in the picture is 12 cm across and 19 cm high. What is its volume?
- A. 228π cm³
- B. 2736π cm³
- C. 684π cm³
- D. 114π cm³
Choose the right answer
Answer:
3.The cylinder in the picture has a volume of 180π cm³ and a base radius of 6 cm. How high is it, in cm?
Answer:
4.Using your calculator's π key, find the volume of the cylinder in the picture: radius 8 cm, height 11 cm. To 3 significant figures, what is it, in cm³?
Answer:
5.The cylinder in the picture has a volume of 112π cm³ and a height of 7 cm. What is its base radius r, in cm?
Answer:
All the answers
- 1. 1000 π cm³
- 2. C. 684π cm³
- 3. 5 cm
- 4. 2210 cm³
- 5. 4 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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