Question

The minute hand of a clock is `sqrt(21)` cm long. Find the area described by the minute hand on the face of the clock between 6 a.m. and 6.05 a.m.

Answer 1

In 60 minutes, minute hand of a clock move through an angle of `360^(@)`
`:.` In 5 minutes hand will move through an angle `= (360^(@))/(60) xx 5 = 30^(@)`
Now, `r = sqrt(21) cm and theta = 30^(@)`
Area of sector described by the minute hand between 6 a.m. and 6.05 a.m.
`= (pi r^(2) theta)/(360^(@)) = (22)/(7) xx (sqrt(21))^(2) xx 30^(@) xx (1)/(360^(@)) = 5.5 cm^(2)`