Mathematics, 14.01.2021 16:50 TristonC1680
1. Sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. (a) How fast is the volume increasing when the radius of the base is 3 ft and is increasing at a rate of 3 in/min
Answers: 2
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]](/tpl/images/1035/4519/c15a3.png)
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]](/tpl/images/1035/4519/8747d.png)
![\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}]](/tpl/images/1035/4519/112e0.png)
    ![\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}]](/tpl/images/1035/4519/9aa77.png)
  (1)   
= 3 in/min
![\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]](/tpl/images/1035/4519/a14e9.png)
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