Question 613427
Water is dripping slowly through the bottom of a small
conical cup that is 4 cm across and 6 cm deep. The cup loses half a cubic centimetre of water each
minute. How fast is the water level dropping at the moment when the water is 3 cm deep?
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{{{Vol = pi*r^2*h/3}}}
r = 2, h = 6
r = h/3
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{{{Vol = pi*(h/3)^2*h/3 = pi*h^3/27}}}
{{{dV/dt = (pi*h^2/9)*(dh/dt)}}}
@ h = 3: {{{1 cm/min = (pi*9/9)*(dh/dt)}}}
{{{dh/dt = 1/pi}}} cm/min