SOLUTION: Water is poured into a conical paper cup at the rate of 3/2 in^3/sec . If the cup is 6 inches tall and the top
has a radius of 3 inches, how fast is the water level rising when th
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Question 994582: Water is poured into a conical paper cup at the rate of 3/2 in^3/sec . If the cup is 6 inches tall and the top
has a radius of 3 inches, how fast is the water level rising when the
water is 3 inches deep?
The water level is rising at a rate of____
Thank you
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The volume of a cone of height and radius is given by
.
I am not going to keep mentioning units,
but time, is understood to be measured in seconds;
and are understood to be measured in inches,
and is understood to be in cubic inches.
The cup is filling at a rate of .
As the water is filling the conical paper cup,
the water is in the shape of a similar cone,
with a radius to height ratio of ,
so .
The volume of water in the cup as a function of the water-cone height is
.
The inverse function is
When , ;
, and
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