- #1
nameVoid
- 241
- 0
a tank the shape of a cylinder has base radius 3/2 m and height 6m lies horizontal and has a spout of length 1m. Find the work to pump all of the water out of the tank.
placing one end of the tank at the origin and using rectangular cross sections. I have attempted to first calculate the bottom half for negative y values and then add it to the top
[tex]
C=9.8*10^3
[/tex]
[tex]
C\int_{-\frac{3}{2}}^{0}12\sqrt{\frac{9}{4}-y^2}(\frac{5}{2}+y)dy +C\int_{0}^{\frac{3}{2}}12\sqrt{\frac{9}{4}-y^2}(\frac{5}{2}-y)dy
[/tex]
also similar case here, A tank with semicircle base radius 2ft and height 8ft lies horizontl and has spout 1ft
placing the center of the circle at the orgin
[tex]
C=62.5
[/tex]
[tex]
C\int_{-2}^{0}16\sqrt{4-y^2}(1+y)dy
[/tex]
it looks likes the text is taking the limits of integration here from 0 to 2 I don't understand why
placing one end of the tank at the origin and using rectangular cross sections. I have attempted to first calculate the bottom half for negative y values and then add it to the top
[tex]
C=9.8*10^3
[/tex]
[tex]
C\int_{-\frac{3}{2}}^{0}12\sqrt{\frac{9}{4}-y^2}(\frac{5}{2}+y)dy +C\int_{0}^{\frac{3}{2}}12\sqrt{\frac{9}{4}-y^2}(\frac{5}{2}-y)dy
[/tex]
also similar case here, A tank with semicircle base radius 2ft and height 8ft lies horizontl and has spout 1ft
placing the center of the circle at the orgin
[tex]
C=62.5
[/tex]
[tex]
C\int_{-2}^{0}16\sqrt{4-y^2}(1+y)dy
[/tex]
it looks likes the text is taking the limits of integration here from 0 to 2 I don't understand why