www.stewartcalculus.com/data/ESSENTIAL%20CALCULUS%20Early%20Transcendentals/upfiles/projects/ess_wp_0706a_stu.pdf
i have question on number 4 i dont know were to begin or dont know how to set it up i read the problem 5 times and still seem confused by it .i know you need to use separable equation.
Not all water tanks are shaped like cylinders. Suppose a tank has cross-sectional area A(h) at height h. Then the volume of water up to height h is given by
\(\displaystyle V(h)\,\, =\,\, \int_0^h\,\, A(u)\,\, du\)
and so the Fundamental Theorem of Calculus gives dV/dh = A(h). It follows that
\(\displaystyle \frac{dV}{dt}\, =\, \frac{dV}{dh}\, \frac{dh}{dt}\, =\, A(h)\,\, \frac{dh}{dt}\)
and so Torricelli’s Law becomes
\(\displaystyle A(h)\,\, \frac{dh}{dt}\, =\, -a\, \sqrt{2\, g\, h} \)
(a) Suppose the tank has the shape of a sphere with radius 2 m and is initially half full of
water. If the radius of the circular hole is 1 cm and we take g=10 m/s
2, show that h satisfies the differential equation
\(\displaystyle (4h\, -\, h^2)\, \frac{dh}{dt}\, =\, -0.0001\, \sqrt{20\,h}\)
(b) How long will it take for the water to drain completely?
I believe I've got the problem correct. In any case if the tank has the shape of a sphere, which is the cross sectional area? Please show your work and where you are stuck so we can help. You should also read
http://www.freemathhelp.com/forum/threads/77972-Read-Before-Posting!!