Consider a set of points `R` in the space 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=0a n dx-y+2z=0.` a. The volume of the bounded figure by points `b . R c.` d. and the planes is `e . f.(g . h. 103sqrt(i .3j .)k . l.)pim .` n. cube units. o. The area of the surface formed by the set of points `p . R q.` r. is `s . t.(u . v. 20pi//sqrt(w .6x .)y . z.)a a .` bb. sq. units. cc. The volume of the bounded figure by the set of points `d d . R ee.` ff. and the planes is `g g . hh.(i i . jj. 20pi//sqrt(k k .6l l .)m m . nn.)o o .` pp. cubic units. qq. The area of the curved surface formed by the set of points `r r . R ss.` tt. is `u u . vv.(w w . xx. 10//sqrt(y y .3z z .)a a a . bbb.)pic c c .` ddd. sq. units.

Options

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

Answer

b,c

Explanation

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)`