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10 Nov 2019
a) Find the average value f of thefunction \(f(x,y,z)=\sqrt{x^{2}+y^{2}+z^{2}}\) defined atall points of the halfball \(x^{2}+y^{2}+z^{2}<=1\) withz<=0.
b) A capped reservoir is bounded by thesurfaces: \(S1:x^{2}+y^{2}=9\) , \(S2: y+z =5\) , \(S3: z=1\) Calculate the reservoirvolume.
c) Consider three cylinders in the dimensionalspace: \(x^{2}+y^{2}=1\) , \(y^{2}+z^{2}=1\) and \(x^{2}+z^{2}=1\) . Make a sketch ofthe intersection of the three cylinders and find the volume of thesolid bounded by the three cylinders.
a) Find the average value f of thefunction \(f(x,y,z)=\sqrt{x^{2}+y^{2}+z^{2}}\) defined atall points of the halfball \(x^{2}+y^{2}+z^{2}<=1\) withz<=0.
b) A capped reservoir is bounded by thesurfaces: \(S1:x^{2}+y^{2}=9\) , \(S2: y+z =5\) , \(S3: z=1\) Calculate the reservoirvolume.
c) Consider three cylinders in the dimensionalspace: \(x^{2}+y^{2}=1\) , \(y^{2}+z^{2}=1\) and \(x^{2}+z^{2}=1\) . Make a sketch ofthe intersection of the three cylinders and find the volume of thesolid bounded by the three cylinders.
Nestor RutherfordLv2
27 Feb 2019
