Question 34 of 42intermediate🔧 ApplyNumerical3 marks

If the wheel of a bicycle has a diameter of 60 cm, find how far a cyclist will have travelled after the wheel has rotated 100 times.

Correct Answer

18857.14 cm or 188.57 m

Exercise: END-OF-CHAPTER EXERCISES | Q: 7 | (Page 32)
For More Understanding

Explanation

The distance a cyclist travels in one complete rotation of the wheel is equal to the circumference of the wheel. The context provides the formula for the circumference of a circle as 2 × π × r and instructs using 22/7 for π. By calculating the circumference and multiplying it by the total number of rotations (100), we find the total distance travelled.

Solution Steps

  1. Step 1: Find the radius of the wheel. The diameter is given as 60 cm. Therefore, the radius r = 60 / 2 = 30 cm.

  2. Step 2: Calculate the distance covered in one rotation. This distance equals the circumference of the wheel. Using the formula 2 × π × r and π ≈\approx 22/7, Circumference = 2 × (22/7) × 30 = 1320/7 cm.

  3. Step 3: Calculate the total distance for 100 rotations. Total Distance = 100 × Circumference = 100 × (1320/7) = 132000/7 cm.

  4. Step 4: Convert to meters. 132000/7 cm ≈\approx 18857.14 cm. Dividing by 100 gives 188.57 m.

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