Formula sheet
Volume of cylinder
πr²h is given on the exam formula sheet. You must still use the radius (not diameter), square it, and not confuse volume (cm³) with surface area.
What the symbols mean
- r Radius of the circular base (length unit).
- h Height of the cylinder (length unit).
- π Pi ≈ 3.142 or 22/7.
Given in the exam, or memorise?
πr²h is given on the exam formula sheet. You must still use the radius (not diameter), square it, and not confuse volume (cm³) with surface area.
Why it works
A cylinder is a circle pushed up through a height.
- The base is a circle of area πr².
- Volume of any uniform solid is base area × height.
- So volume = πr² × h = πr²h.
Worked example 1
Find the volume of a cylinder with radius 7 cm and height 10 cm. (Use π = 22/7)
- Volume = πr²h
- = 22/7 × 7² × 10
- = 22/7 × 49 × 10
- = 154 × 10 = 1540
Worked example 2
A cylinder of radius 7 cm has volume 3080 cm³. Find its height.
(Use π = 22/7)
- Volume = πr²h
- πr² = 22/7 × 49 = 154
- 3080 = 154 × h
- h = 3080 ÷ 154 = 20
Where students go wrong
- Using the diameter in place of the radius.
- Forgetting to square r, computing πrh instead of πr²h.
- Confusing this volume with the surface-area formula.
- Answering in cm² instead of cm³.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
How is volume of a cylinder different from its surface area?
Volume πr²h measures the space filling the cylinder, in cm³. Surface area 2πr² + 2πrh measures the material covering its outside, in cm².
Volume multiplies one area by a height; surface area adds several areas. The cubic unit versus square unit is the fastest way to tell which one a question wants.
The tank's diameter is given. How do I use it?
Convert to radius by halving before you substitute, because πr²h uses r. A tank of diameter 14 cm has r = 7 cm, so volume = π × 7² × h.
If you place 14 into r you get a volume four times too big, since the radius is squared. Halve first, then square.
Can I find the height if I know the volume?
Yes. Work out πr² first, then divide the volume by it, because volume = πr² × h.
For example volume 3080 cm³ with πr² = 154 gives h = 3080 ÷ 154 = 20 cm. It is the same formula rearranged so that height is the unknown you solve for.