Question

The minute hand of a certain clock is 6 in long. Starting from the moment when the hand is pointing straight up, how fast is the area of the sector that is swept out by the hand increasing at any instant during the next revolution of the hand?

Answer 1

area of a sector ...

A = \frac{1}{2}r^2 \theta

take the derivative w/r to time, t ...

\frac{dA}{d\theta} = \frac{1}{2}r^2 \frac{d\theta}{dt}

... a minute hand of a clock moves at the rate of 2pi radians per hour.

finish up.

Answer 2

ohhhh, the minute hand moves at 2pi/60mins, okay i can finish it up, thanks !

Answer 3

Welcome :)