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Consider the cylindrical tank in Example 4 that has a height of 10 m and a radius of 5 m. Recall that if the tank is full of water, then
10. The work required to empty the tank if it is half full
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- We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can". The height of the cylinder is 8 inches. A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (it's two circles for the top and bottom plus a rolled up rectangle for the side). Part A: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A(r)=2πr^2+16 πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined? I believe the answer to this part is "All real numbers" Part B: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A(r), i.e to turn A as a function of r into. r as a function of A. For this part nothing I have written is working. Any help…arrow_forwardThe height of the cylinder is 4 inches. We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can". A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A=2πr2+2πrh (it's two circles for the top and bottom plus a rolled up rectangle for the side). Part a: Assume that the height of your cylinder is 4 inches. Consider A as a function of r, so we can write that as A(r)=2πr2+8πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined? Part b: Find the inverse function to A(r). Your answer should look like r="some expression involving A". r(A)= Hints: To calculate an inverse function, you need to solve for r. Here you could start with A=2πr2+8πr. This equation is the same as 2πr2+8πr−A=0. Do you recognize this as a quadratic equation…arrow_forwardA water reservoir has the shape of a right circular cone with its circular base of radius R = 160 m at ground level (z = 0 m). Rain fills the reservoir over the winter; when full, the reservoir depth is h = summer, water from the reservoir is pumped up to ground level for drinking, irrigation, etc. At the end of the summer, the volume of water left in the reservoir is only 3/7 of its full capacity. %3D 70 m. In (a) Find the depth of the water in the reservoir at the end of the summer. Answer: Depth = 52.776 m (b) Find the total work done to lift water out of the reservoir during the summer. Answer: W = 54461207640 J. (Recall the density of fresh water: p = 1000 kg/m.)arrow_forward
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