The distance covered by a tire of 84 cm radius in 4 revolutions is

Question

The distance covered by a tire of 84 cm radius in 4 revolutions is

1. A. 1056 cm
2. B. 2112 cm (Correct answer)
3. C. 840 cm
4. D. 1840 cm

Correct Answer

Option B — 2112 cm

Detailed Solution & Explanation

The correct answer is 2112 cm.

Key Points

• In one revolution, a wheel covers a distance equal to its circumference:
  • $C = 2\pi r = 2 \times \frac{22}{7} \times 84$
• Since $84 \div 7 = 12$:
  • $C = 2 \times 22 \times 12 = 528 \text{ cm}$
• Distance in 4 revolutions:
  • $D = 4 \times 528 = 2112 \text{ cm}$

Shortcut Trick

• Combine the constants before multiplying: distance $= 2\pi r n = 2 \times \frac{22}{7} \times 84 \times 4$. Cancel $84/7 = 12$ first, then $2 \times 22 \times 12 \times 4 = 2112$. Cancelling before multiplying keeps every number small.

Additional Information

• The standard wheel relationship:
  • $\text{Distance} = \text{Number of revolutions} \times 2\pi r$
• Rearranged, it answers the two other common forms of this question:
  • Revolutions $=\dfrac{\text{Distance}}{2\pi r}$
  • Radius $=\dfrac{\text{Distance}}{2\pi \times \text{Revolutions}}$
• Distractor check: 1056 cm is the answer for 2 revolutions, and 528 cm for one — always confirm the number of revolutions asked.