# The hour hand of a clock is 6 cm long.

Question:

The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is

(a) $2.75 \mathrm{~cm}^{2}$

(b) $5.5 \mathrm{~cm}^{2}$

(c) $11 \mathrm{~cm}^{2}$

(d) $10 \mathrm{~cm}^{2}$

Solution:

Hour hand moves $\left(\frac{1}{2}^{\circ}\right)$ in one minute.

So, area,

$=\frac{1}{2}\left(r^{2}\right)\left(\frac{\theta}{180} \pi\right)$

$=\frac{1}{2}(36)\left(\frac{35}{2(180)} \pi\right)$

$=5.5 \mathrm{~cm}^{2}$