A resevoir has the shape of an inverted cone with altitude 6m and diameter at the top 18m. Water runs in at
. At the instant the maximum depth is 4m, determine the following.
a) the rate of increase of depth [completed Answer for
is
when h=4m
b) the rate of increase of wetted surface area of the reservoir [answer is
b) since i am not given
or
the only way i can solve for surface area is if i put r and s in terms of h then differentiate, plug in values and hopefully get the answer.
SA =
SA =
SA =
which is definenty not the answer. So what am i doing wrong???? my logic seems fine... and also I even tried direct subsitution for s in the SA formula and still didnt get the right answer. I am not given
or
the only thing i know is to write s and r in terms of h and even then as u see is still the incorrect answer. Please help. Im in dire need of assistance.
And if u are wondering how i got the slant height. Its from using phythagorean theorum and substituting
Then using phythagorean theorum:
And also the relation of r:h is from making a diagram. I do not know how to create pictures in LateX but from reading this problem and making a diagram this is what you should get: