4. A pool is in the shape of an octagon (see Figure I in the diagrams page, measurements in feet). (a) Place the octagon
Posted: Mon Jul 11, 2022 12:45 pm
4. A pool is in the shape of an octagon (see Figure I in thediagrams page, measurements in feet).(a) Place the octagon in the xy−plane, with the center of theoctagon at the origin, (0, 0), and one of the vertices of theoctagon at the point on the x−axis,(10, 0). See Figure II in theattached diagrams page. Use the techniques of area between curves(integrals), to find the area of the shaded triangle in thediagram. This will give you 1/8 of the total area of theoctagon.
(b) Multiply your answer in part (a) by 8 to get the total areaof the octagon.
(c) Suppose a pool has the shape of the octagon above and anoverall height of10 feet (See Figure I in the diagrams page).Further suppose that the depthof the water in the pool is 9 feet deep. Find the work done to pumpall of the water out of the pool. First, set this up as a RiemannSum, finding the work Wi required to pump the ith slice of water,of width ∆x, out of the pool. Then, set up the correspondingintegral and integrate to find the work done to pump all of thewater out of the pool. Use the fact that water
(b) Multiply your answer in part (a) by 8 to get the total areaof the octagon.
(c) Suppose a pool has the shape of the octagon above and anoverall height of10 feet (See Figure I in the diagrams page).Further suppose that the depthof the water in the pool is 9 feet deep. Find the work done to pumpall of the water out of the pool. First, set this up as a RiemannSum, finding the work Wi required to pump the ith slice of water,of width ∆x, out of the pool. Then, set up the correspondingintegral and integrate to find the work done to pump all of thewater out of the pool. Use the fact that water