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Numerade Educator



Problem 35 Medium Difficulty

If the minute hand of clock has length $ r $ (in centimeters), find the rate at which it sweeps out area as a function of $ r, $


$\frac{d A}{d t}=\frac{\pi}{60} \cdot r^{2}$


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Video Transcript

we have a question in which it is being said that if a minute hand of a clock has learned are so if this is a clock minute 10 okay are in centimeters. So we have to find rate at which it strips out area as a function of our. Okay so let us suppose this data this is data and Okay ah Area that in this area. So area sector area of sector is always by our square theater divided by 300 60 degrees. So we have to find the er by the data. Sorry D. A. By the theater. D. V. D. T. Because the rate we have to find out. Okay so do you buddy will be equal to buy 3 to By 360° and to our by. Okay. No one thing to be very sure that one thing to be very sure that are is constant because it is radius which cannot be changed. So this is our Martita could be changed. So we'll be differentiating this with respect to variable which is uh we will be differentiating with respect to time to the variables like D. By D. T. By our square to to buy 360 degree all our constant but Peeta is not constant. So Pie are square 360 degree into the theater by DT. So area rate of change of area. The ability will be equal to buy a square By 360° defeated by DT. Where he died. The angle stripped by the uh what we say, angle swept by them in a tent. Thank you.