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A gasoline storage tank is in the shape of a right circular cylinder with a hemisphere at each end, as shown in Fig. 29.7. Express the volume $V$ of the tank in terms of $r$ and $h$ and then evaluate the volume for $r=3.75 \mathrm{ft}$ and $h=12.5 \mathrm{ft}$.
Calculus 3
Chapter 29
Partial Derivatives and Double Integrals
Section 1
Functions of Two Variables
Partial Derivatives
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way have a cylindrical tank and we know that the volume of a cylinder is pi r squared h and we're given that the radius in the height together have to be 50. That must mean the height is 50 minus are we also know that the volume is 40,000. So we have the equation. 40,000 equals high are square times, 50 minus are for the height. What we can do is in a graphing calculator we can set. One equation is your Why one and the other is your y two and find the intersection of them. So I'm gonna jump over and do this with dust most so one equation is 40,000. You need a wide calls by the late. And the 2nd 1 is our, um Hi. Well, minute call. Since this one dream, I'm gonna call it acts high times, pecs where I'm 50 minus x. Then we're looking for the intersection of the 2 40 thousands way up there. Way, way up. There we are. And you can zoom in the window where this is feasible. And now these air possible values for a radius and negative 14 for the radius doesn't make sense, so we're not gonna include that one. But 20.93 in 43.1 seven do so possible. Dimensions would include a radius of about 20.93 which then would have ah, height of 50 minus 29. 20.93 It should be about 29.7 or we saw the other intersection. Was that about 43.1 70 which would then have a height of about 6.83? Because that's 50 minus 43 0.17
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