1.

Consider a set of point Rin which is at a distance of 2 units from the line (x)/(1)= (y-1)/(-1)= (z+2)/(2) between the planes x-y+2z=3=0 and x-y+2z-2=0.

Answer»

The volume of the bounded figure by POINTS R and the planes is `(10//3sqrt3)pi` cube units.
The AREA of the curved surface formed bythe set of points R is `(20 pi //sqrt6)` sq.units.
The volume of the bounded figure by the set of points R and the planes is `(20pi//sqrt6)` cubic units.
The area of the curved surface formedby the set of points R is `(10//sqrt3)pi` sq. units.

Solution :Distance between the planes is `h= 5//sqrt6`.
ALSO the figure formed is a CYLINDER, whose radius is `r=2` units.
Hence, the volume of the cylinder is
`""pir^(2)h= pi(2)^(2)*(5)/(sqrt6)= (20pi)/(sqrt6)` cubic units.
Also the curved surface area is
`""2pirh= 2pi(2)*(5)/(sqrt(6))= (20pi)/(sqrt6)`


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