4. A pool is in the shape of an octagon (see Figure I, mea- surements in feet). (a) Place the octagon in the xy-plane, w

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4 A Pool Is In The Shape Of An Octagon See Figure I Mea Surements In Feet A Place The Octagon In The Xy Plane W 1 (146.65 KiB) Viewed 41 times

4. A pool is in the shape of an octagon (see Figure I, mea- surements in feet). (a) Place the octagon in the xy-plane, with the center of the octagon at the ori- gin, (0, 0), and one of the vertices of the octagon at the point on the x-axis, (10, 0). See Figure II in the attached diagrams. Use the techniques of area between curves (integrals), to find the area of the shaded triangle in the diagram. This will give you 1/8 of the total area of the octagon. b) Multiply your answer in part (a) by 8 to get the total area of the octagon. (c) Suppose a pool has the shape of the octagon above and an overall height of 10 feet (See Figure I in the diagrams page). Further suppose that the depth of the water in the pool is 9 feet deep. Find the work done to pump all of the water out of the pool. First, set this up as a Riemann Sum, finding the work Wi required to pump the ith slice of water, of width AX, out of the pool. Then, set up the corresponding integral and integrate to find the work done to pump all of the water out of the pool. Use the fact that water weighs 62.5 lbs/ft3. Figure I' 10 ft lo ft. HOIDE 9 ft. 10 ft Figure II : (10,0)