The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes?

The correct answer is (B) 6.28 cm.

• Given Data & Formula: The length of the minute hand serves as the radius ($r$) of the circular path described by its tip, so $r = 1.5$$\text{ cm}$. In 60 minutes, the minute hand completes one full revolution, covering a distance equal to the circumference of the circle ($2$$\pi$ r). The distance covered in 40 minutes represents the arc length corresponding to an angle of 40 minutes out of 60 minutes.
• Step-by-Step Calculation: The fraction of the hour completed in 40 minutes is $\frac{40}{60}=\frac{2}{3}$$\frac{40}{60}$ = $\frac{2}{3}$. Therefore, the distance moved by the tip in 40 minutes is given by $\frac{2}{3}\times 2\pi r$$\frac{2}{3}$ $\times$ 2$\pi$ r. Substituting the values: $\text{Distance}=\frac{2}{3}\times 2\times \frac{22}{7}\times 1.5$$\text{Distance}$ = $\frac{2}{3}$ $\times$ 2 $\times$ $\frac{22}{7}$ $\times$ 1.5. Calculating this yields: $\frac{2}{3}imes2imes\frac{22}{7}imes\frac{3}{2}=\frac{44}{7}\approx 6.285\text{ cm}$$\frac{2}{3}$ imes 2 imes $\frac{22}{7}$ imes $\frac{3}{2}$ = $\frac{44}{7}$ $\approx$ 6.285$\text{ cm}$, which rounds to 6.28 cm.
• Option Verification: Option (A) 5.28 cm, Option (C) 7.28 cm, and Option (D) 4.28 cm are derived from incorrect fractional proportions or computational errors in evaluating $\frac{44}{7}$$\frac{44}{7}$. Hence, option (B) is the only accurate mathematical solution.