Question #2104

Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm2?
____________ cm2/s

Expert's answer

<img src="/cgi-bin/mimetex.cgi?V%20=%20h%5E2%20%5C%5C%20%5CDelta%20V%20=2h%20%5CDelta%20h%20%5C%20%7C%5Cdiv%20%5CDelta%20t%5C%5C%20%5Cfrac%7B%5CDelta%20V%7D%7B%5CDelta%20t%7D%20=2h%20%5Cfrac%7B%5CDelta%20h%7D%7B%5CDelta%20t%7D%5C%5C%20h%28V=36%29=%20%5Csqrt%7B36%7D%20=%206%20%5C%5C%20%5Cfrac%7B%5CDelta%20V%7D%7B%5CDelta%20t%7D%20=2%20%5Ccdot%206[cm]%20%5Ccdot%203[cm/s]%20=%2036%20%5C%20[cm%5E2/s]." title="V = h^2 \\ \Delta V =2h \Delta h \ |\div \Delta t\\ \frac{\Delta V}{\Delta t} =2h \frac{\Delta h}{\Delta t}\\ h(V=36)= \sqrt{36} = 6 \\ \frac{\Delta V}{\Delta t} =2 \cdot 6[cm] \cdot 3[cm/s] = 36 \ [cm^2/s].">

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