The rate at which water is poured into the cup of radius 10 cm when the water level is 8 cm is 100.48 cm^3/sec.
Since we know the volume of a cone is: V=πr²h/3, where h is the height and r is the radius of the base of the cone .Here the slope of h and r is: h/r= 20/10 =2 ,Now we can convert the formula for the volume of the cone with just one variable :
V=π(h/2)²h/3
=πh³/12
Now differentiation of both sides with respect to time t, we get
V'=3πh²h'/12, where h' is the rate of change of height
=πh²h'/4
now substituting the know values in the above formula , we get
V= 3.14*(8)²*2/4 = 32 *3.14 = 100.48 cm³/sec .
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A conical paper cup is 20 cm tall with a radius of 10 cm. The cup is filled with water so that the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cup when the water level is 8 cm?
