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.
Answer & explanation
Correct answer: option 1
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 × \(\frac{ 270 }{360 }\)
= $\frac{6600}{7} \mathrm{~cm}^2$