A pool is in the shape of an octagon (see Figure I in the diagrams page, mea- surements in feet). (a) Place the octagon
Posted: Sat Jul 09, 2022 2:21 pm
A pool is in the shape of an octagon (see Figure I in thediagrams page, mea-surements in feet).(a) Place the octagon in the xy−plane, with the center of theoctagon at the ori-gin, (0, 0), and one of the vertices of the octagon at the point onthe x−axis,(10, 0). See Figure II in the attached diagrams page. Use thetechniques ofarea between curves (integrals), to find the area of the shadedtriangle inthe diagram. This will give you 1/8 of the total area of theoctagon.
(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 thatthe depthof the water in the pool is 9 feet deep. Find the work done to pumpallof the water out of the pool. First, set this up as a Riemann Sum,findingthe work Wi required to pump the ith slice of water, of width ∆x,out ofthe pool. Then, set up the corresponding integral and integrate tofind thework done to pump all of the water out of the pool. Use the factthat waterweighs 62.5 lbs/ft3.
(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 thatthe depthof the water in the pool is 9 feet deep. Find the work done to pumpallof the water out of the pool. First, set this up as a Riemann Sum,findingthe work Wi required to pump the ith slice of water, of width ∆x,out ofthe pool. Then, set up the corresponding integral and integrate tofind thework done to pump all of the water out of the pool. Use the factthat waterweighs 62.5 lbs/ft3.