The figure shows the surface created when the cylinder y^2+Z^2=1 intersects the cylinder x^2+Z^2=1. Find the area of this surface.The figure is something like:FSP02510400011.jpgFSZ

sodni3 2020-12-16 Answered

The figure shows the surface created when the cylinder y2+Z2=1 intersects the cylinder x2+Z2=1. Find the area of this surface.
The figure is something like:
image

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Expert Answer

stuth1
Answered 2020-12-17 Author has 97 answers
Note that the given cylinder will intersect at four congruent surfaces. e. equal in area. So we need to find the area of only one surface and then multiply it by 4.
First, we find the area of the face of the surface that intersect the positive y axis. So the surface lies above the region x2+z2=1 then z=f(x,z)=1z2
=x2+z21fx2+fz2+1dA
=x2+z21z21z2+1dA
=111z21+z211z2dxdz
=40101z211z2dxdz
=limt1+40t01z211z2dxdz
=limt1+40t1dt
=4
Hence the total area of the intersected surface is 4×4=16
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