If the diameter of a car tyre is 56 cm, then:
- (i) How far does the car need to travel for the tyre to complete one revolution?
- (ii) How many revolutions does the tyre make if the car travels 10 km?
Answer: (i) 176 cm (ii) 1 000 000 ÷ 176 ≈ 5682 revolutions
Step-by-step solution
Idea: Each turn of the wheel rolls out one circumference along the road. Distance ÷ circumference = number of turns (use the same unit for both).
(i) How far does the car need to travel for the tyre to complete one revolution?
- In one revolution the car moves forward by one circumference: πd = 227 × 56 = 176 cm.1 mark
176 cm
(ii) How many revolutions does the tyre make if the car travels 10 km?
- 10 km = 10 × 1000 × 100 cm = 1 000 000 cm.½ mark
- Number of revolutions = 1000000176 = 5681.8… ≈ 5682 (5681 complete turns and a bit more).1½ marks
about 5682 revolutions
(i) 176 cm (ii) about 5682 revolutions (5681.8)
Check: 5681.8 × 176 cm ≈ 1 000 000 cm = 10 km ✓.
Answer to write in the exam
(i)
Distance in 1 revolution = πd = 227 × 56
∴ Distance = 176 cm
(ii)
10 km = 1 000 000 cm
Revolutions = 1000000176 = 5681.8…
∴ About 5682 revolutions
Common mistakes that cost marks
- Using the radius 56 cm, i.e. 2π × 56. 56 cm is the diameter.
- Dividing 10 by 176 without changing km to cm.
- Writing 1 km = 1000 cm. 1 km = 1000 m = 100 000 cm.
How this can come in the exam
MCQ (1 mark)
A wheel of diameter 70 cm makes 500 revolutions. The distance covered is (use π = 227)
- 1.1 km
- 2.2 km
- 0.55 km
- 1.76 km
Show answer
(A) 1.1 km
One turn = 227 × 70 = 220 cm; 500 × 220 = 110 000 cm = 1.1 km.
Try one yourself
A bicycle wheel has diameter 42 cm. How many complete revolutions does it make in 1.32 km? (Use π = 227.)
Show answer
One turn = 227 × 42 = 132 cm; 132 000 ÷ 132 = 1000 revolutions.
More questions like this
- Find the total perimeter of all the petals in each of the given flowers.
- The ratio of the perimeters of two circles is 5:4. What is the ratio of their radii?
- What happens if the parallelogram is ‘thin’ (see the figure) and the foot of the perpendicular from C to AD does not lie on side AD? The construction then does not seem to work. How do we fix this ‘gap’?
- The area of a rectangle can be found when we know the lengths of its sides. Is the same true for a parallelogram? That is, can we find the area of a parallelogram when we know the lengths of its sides? Why or why not? (Hint: What happens to the area of a parallelogram if we decrease or increase the angle between the adjacent sides while keeping the lengths fixed?)
- You may wonder, like earlier, is there a gap in our argument? What would we do if angle EFG is obtuse and the triangle were shaped like triangle EFG in the figure? Please work out the answer to this question.