Suppose that a conical container is filled with some amount of fluid. The circular base of...

 

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Suppose that a conical container is filled with some amount of fluid. The circular base of the container sits on the ground. The base of the container has radius 20 meters, and the height of the container is 40 meters. Suppose that y denotes height, in meters, above the bottom of the container. (a) Find a formula A(y) for the area of the horizontal cross-section of the cone at height y. (b) Write, but do not evaluate, an integral giving the volume of the conical container. (c) Suppose that the cone is completely filled with a fluid having density 800 kilograms per cubic meter. Write, but do not evaluate, an integral giving the total mass of the fluid in the container. (d) Write, but do not evaluate, an integral giving the total work needed to pump the fluid to the top of the container. (e) Suppose that the fluid in the container only reaches a depth of 7 meters. Write, but do not evaluate, an integral giving the total work needed to pump the fluid to the top of the container. Suppose that a conical container is filled with some amount of fluid. The circular base of the container sits on the ground. The base of the container has radius 20 meters, and the height of the container is 40 meters. Suppose that y denotes height, in meters, above the bottom of the container. (a) Find a formula A(y) for the area of the horizontal cross-section of the cone at height y. (b) Write, but do not evaluate, an integral giving the volume of the conical container. (c) Suppose that the cone is completely filled with a fluid having density 800 kilograms per cubic meter. Write, but do not evaluate, an integral giving the total mass of the fluid in the container. (d) Write, but do not evaluate, an integral giving the total work needed to pump the fluid to the top of the container. (e) Suppose that the fluid in the container only reaches a depth of 7 meters. Write, but do not evaluate, an integral giving the total work needed to pump the fluid to the top of the container.