Question

The length of minute hand of a clock is $500$ mm.Find area swept by minute hand during $6.05$ am to $6.40$ am.

Answer 1

we know that the minute hand covers $6^{\circ }$ per minute

For $35$ minutes

$\theta =6\times 35={210}^0$

$\therefore$ area $=\frac{210}{360}\times \pi \times {\left(500\right)}^2{mm}^2$

$=\frac{7\pi }{6\times 2\pi }\times \pi \times 0.5\times 0.5m^2$

$=\frac{7}{12}\pi \times {0.25m}^2=\frac{7\pi }{48}{m}^2$

$=0.4581m^2$