A hemispherical container of radius 2m, when the depth of the liquid of the container is h metres (filling up from bottom),
the volume of liquid V in m^3, is given by 1/3((pi)*h^2)(6-h).
Prove this to be correct.
the volume of liquid V in m^3, is given by 1/3((pi)*h^2)(6-h).
Prove this to be correct.
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Consider the semi-circle centre (0,2) and radius 2 which has equation
x^2+(y-2)^2=4. A horizontal strip thickness dy and radius x is rotated
about the y-axis to give a volume dV=(pi)*x^2*dy=(pi)*(4-(y-2)^2)dy=(pi)*(… dy
Integrate this from y=0 to y=h which you should mange if you are careful.
x^2+(y-2)^2=4. A horizontal strip thickness dy and radius x is rotated
about the y-axis to give a volume dV=(pi)*x^2*dy=(pi)*(4-(y-2)^2)dy=(pi)*(… dy
Integrate this from y=0 to y=h which you should mange if you are careful.