The minute hand of a clock is $20 \mathrm{~cm}$ long. Find the area on the face of the clock swept by the minute hand between 8 a.m. and $8: 45$ a.m.

$\frac{6600}{7} \mathrm{~cm}^2$

We know that,

Area of a sector = πr² × \(\frac{ θ }{360}\)

We have,

The length of the minute hand of a clock = 20 cm

As we know in the 1-minute angle made by the minute hand = 6°

So, in 45 min the minute hand will make 45 × 6 = 270°

Area = π × 20² × \(\frac{ 270 }{360   }\)

= \(\frac{22}{7}\) × 400 × \(\frac{ 270 }{360   }\)

=  $\frac{6600}{7} \mathrm{~cm}^2$