Let S be the solid bounded by the surfaces z=2sqrt(x^2 + y^2) and z=2. Suppose that...

Let S be the solid bounded by the surfaces z=2sqrt(x^2 + y^2) and z=2. Suppose that thedensity of S at (x,y,z) is equal to z.

Set up an integral for the mass of S using spherical coordinates.

Solutions

Expert Solution

mass=

in spherical cordinates=

and

also

so z=2sqrt(x^2 + y^2) means or this is half angle of the cone so if we integrate using the limits 0<theta< we actually get half the required .(so we should multiply by 2)

and 0<r<5^(.5) ,

so=

Nb:

and

the limit of r is obtained as at the z=2 = 2sqrt(x^2 + y^2) so x^2+y^2=1

in spherical cordinates r^2=x^2+y^2+z^2 so r^2= 1^2+2^2= 5 (as z=2 and x^2+y^2=1 )

milcah answered 1 year ago

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