The minute hand of a clock is 8 cm long. Find the area swept by the minute hand between 8.30 a.m. and 9.05 a.m.

Length of the minute hand (radius of the circle) = 8 cm

Time interval between 9.05 a.m. and 8.30 a.m. = 35 minutes

Area swept by the minute hand in 1 hr = πr²

$= \dfrac{22}{7} \times 8^2\\[1em] = \dfrac{22}{7} \times 64\\[1em] = \dfrac{1,408}{7} \text{ cm}^2$

Area of the circle in 60 minutes = $\dfrac{1,408}{7}$ cm²

Area of the circle in 1 minute = $\dfrac{1,408}{7 \times 60}$ cm²

= $\dfrac{352}{105}$ cm²

Area of the circle in 35 minutes = $\dfrac{352 \times 35}{105}$ cm²

= $\dfrac{352}{3}$ cm²

= $117\dfrac{1}{3}$ cm²

Hence, the area swept by the minute hand between 8:30 a.m. and 9:05 a.m. is $117\dfrac{1}{3}$ cm².