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sineoko [7]
3 years ago
12

Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always threethree times its height. Supp

ose the height of the pile increases at a rate of 22 cm divided by scm/s when the pile is 1616 cm high. At what rate is the sand leaving the bin at that​ instant?
Physics
1 answer:
hammer [34]3 years ago
5 0

Answer:

159241.048 cm³/s

Explanation:

r = Radius = 3×height = 3h

h = height = 16 cm

Height of the pile increases at a rate = \frac{dh}{dt}=22\ cm/s

\text{Volume of cone}=\frac{1}{3}\pi r^2h\\\Rightarrow V=\frac{1}{3}\pi (3h)^2h\\\Rightarrow V=3\pi h^3

Differentiating with respect to time

\frac{dv}{dt}=9\pi h^2\frac{dh}{dt}\\\Rightarrow \frac{dv}{dt}=9\pi 16^2\times 22\\\Rightarrow \frac{dv}{dt}=159241.048\ cm^3/s

∴ Rate is the sand leaving the bin at that​ instant is 159241.048 cm³/s

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