ShapesProperties
- 2 flat circular faces and 1 curved face.
- 2 curved edges and no corners.
- Every slice parallel to the ends is a circle of the same radius.
- Unrolled, the curved surface is a rectangle.
Why the formulas work
Volume is base area times height, as for a box: the circular base has area πr² and it is stacked to height h. For the curved surface, picture the label of a tin. Peeled off and laid flat it is a rectangle, as wide as the circumference 2πr and as tall as the tin, so its area is 2πrh. Add the two circular ends for the total surface.
Worked example
Take a cylinder with radius 7 cm and height 10 cm.
- Volume. Volume = πr2h. Here: π × 7 × 7 × 10 = 1,539.38 cm³ (with π = 22/7: 1,540 cm³).
- Curved surface area. Curved surface area = 2πrh. Here: 2 × π × 7 × 10 = 439.82 cm² (with π = 22/7: 440 cm²).
- Total surface area. Total surface area = 2πr(r + h). Here: 2 × π × 7 × (7 + 10) = 747.7 cm² (with π = 22/7: 748 cm²).
Finding a missing measurement
Height = V ÷ πr². A cylinder of volume 1540 cm³ and radius 7 cm has a height of 1540 ÷ 154 = 10 cm, taking π = 22/7. From the curved surface, h = CSA ÷ 2πr: 440 cm² and r = 7 cm give 440 ÷ 44 = 10 cm.
Mistakes to avoid
- Using the diameter as the radius.
- For an open tank or a glass, add only one circular end, not two.
- For a pipe open at both ends, the surface is only the curved part.
Where you see it
Tins, gas cylinders, water pipes, pillars, batteries, glasses, drums and road rollers are cylinders.
Try these
Work each one out, then tap to check.
A cylinder has radius 3.5 cm and height 12 cm. Find its volume, curved surface area and total surface area. Take π = 22/7.
Volume = 462 cm³; Curved surface area = 264 cm²; Total surface area = 341 cm².
A cylinder has radius 14 cm and height 20 cm. Find its volume, curved surface area and total surface area. Take π = 22/7.
Volume = 12,320 cm³; Curved surface area = 1,760 cm²; Total surface area = 2,992 cm².