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A tank pe of an inverted cone (with the point at the bottom). The cone has a diameter of 6 m and a height of 4 m, and it is completely full of water. We're going to calculate the work needed to pump all of the water out over the side of the tank. Assume that acceleration due to gravity is 9.8 m/s², and the density of water is 1000 kg/m³. (a) Draw a picture of the conical tank. We're going to "slice" the water horizontally. Draw one such horizontal slice on your picture.

A tank pe of an inverted cone (with the point at the bottom). The cone has a diameter of 6 m and a height of 4 m, and it is completely full of water. We're going to calculate the work needed to pump all of the water out over the side of the tank. Assume that acceleration due to gravity is 9.8 m/s², and the density of water is 1000 kg/m³. (a) Draw a picture of the conical tank. We're going to "slice" the water horizontally. Draw one such horizontal slice on your picture.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.4: Applications
Problem 8EQ
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A tank full of water has the shape of an inverted cone (with the point at the bottom). The cone has a diameter of 6 m and a height of 4 m, and it is completely full of water. We're going to calculate the work needed to pump all of the water out over the side of the tank. Assume that acceleration due to gravity is 9.8 m/s2, and the density of water is 1000 kg/m³. (a) Draw a picture of the conical tank. We're going to "slice" the water horizontally. Draw one such horizontal slice on your picture. que sexood sds all (b) Calculate the volume of your horizontal slice, then calculate the mass of your slice, the force needed to lift it, and the work needed to lift it all the way to the top. Volume of slice = tot base a Mass of slice = Force to lift slice = Distance to lift slice = Work to lift slice to top = 90-120 (c) Use a definite integral to calculate the total work needed to pump all of the water out over the side of the tank.
Transcribed Image Text:A tank full of water has the shape of an inverted cone (with the point at the bottom). The cone has a diameter of 6 m and a height of 4 m, and it is completely full of water. We're going to calculate the work needed to pump all of the water out over the side of the tank. Assume that acceleration due to gravity is 9.8 m/s2, and the density of water is 1000 kg/m³. (a) Draw a picture of the conical tank. We're going to "slice" the water horizontally. Draw one such horizontal slice on your picture. que sexood sds all (b) Calculate the volume of your horizontal slice, then calculate the mass of your slice, the force needed to lift it, and the work needed to lift it all the way to the top. Volume of slice = tot base a Mass of slice = Force to lift slice = Distance to lift slice = Work to lift slice to top = 90-120 (c) Use a definite integral to calculate the total work needed to pump all of the water out over the side of the tank.
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