Question

The length of the minute hand of a clock is 6 cm. Find the area swept by it when it moves from 7:05 p.m. to 7:40 p.m.

Answer 1

We know that, in 60 minutes, the tip of minute hand moves 360°

In 1 minute, it will move = `360^circ/60` = 6°

∴ From 7:05 pm to 7:40 pm i.e. 35 min, it will move through = 35 × 6° = 210°

∴ Area of swept by the minute hand in 35 min = Area of sector with sectorial angle θ of 210° and radius of 6 cm

= `210/360 xx π xx 6^2`

= `7/12 xx 22/7 xx 6 xx 6`

= 66 cm²