The following figures show different types of cylinders. What is different in each of these cylinders?
Step-by-step solution
Idea: Look at the dotted line joining the centres of the top and bottom circles (the axis) and at the angle it makes with the base.
- Same: both cylinders have two equal circular ends, and every slice parallel to the base is a circle (circular cross-section).½ mark
- First cylinder: its axis stands at 90° to the base (see the right-angle mark). The top is exactly above the bottom. This is a right circular cylinder, like most pipes and tins.1 mark
- Second cylinder: its axis leans, so the top circle is shifted sideways. This is an oblique circular cylinder.½ mark
Check: A stack of coins pushed straight up gives a right cylinder; pushed so that it leans gives an oblique cylinder. Each coin is still a circle ✓.
Answer to write in the exam
Both: two equal circular ends (circular cross-section)
Right circular cylinder: axis ⊥ base
Oblique circular cylinder: axis inclined to base
∴ The difference is the angle between the axis and the base.
Common mistakes that cost marks
- Saying the oblique cylinder’s ends are ellipses. They are circles; the drawing only looks oval because we see them at an angle.
- Saying the difference is the height or the size. Two cylinders can have the same height and the same circular ends and still differ: what changes is the angle the axis makes with the base.
How this can come in the exam
In a right circular cylinder, the axis is
- parallel to the base
- perpendicular to the base
- inclined at 45° to the base
- along a diameter of the base
Show answer
(B) perpendicular to the base
‘Right’ means the axis makes a right angle with the circular base.
Try one yourself
A cylinder is sliced (i) parallel to its base, (ii) along its axis. What shape is each cross-section?
Show answer
(i) a circle; (ii) a rectangle (for a right circular cylinder).
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