Question

Find the distance travelled by the minute hand(length of arc), in 15 minutes if its length is 7 cm.

• A. 10 cm
• B. 11 cm
• C. 14 cm
• D. 21 cm

Answer 1

The correct option is B 11 cm

We know minute hand journey moves in a circular path.
Length of minute hand = radius = 7 cm

The clock represents a whole angle and is 360°
The angle subtended in 5 minute interval =$\frac{360°}{12}$ = ${30}^o$
Hence the angle subtended in 15 minute interval
= 3$\times$${30}^o$ = ${90}^o$

Distance covered by minute hand in 15 minutes
= Length of arc = $\frac{{90}^o}{{360}^o}$$\times$2$\times$pi$\times$r
= $\frac{1}{4}\times 2\times \frac{22}{7}\times$7 = $\frac{2\times 22\times 7}{4\times 7}$ = 11 cm