Why is the following situation impossible? A student's dormitory room measures 3.7 m by 3.7 m, and its ceiling is 2.6 m high. After the student completes his physics course, he displays his dedication by completely wallpapering the walls of the room with the pages from his physics textbook which has 960 pages of text on 480, 0.21 m × 0.28 m sheets. He even covers the door and window

I believe the that it is impossible for him to cover the whole room. Because SA of the room is 65.86 and the SA of a piece of paper is .0588.
And by multiplying it by 480 we get 28.24 and that what makes it impossible to cover the whole room.

Answer Link

AskewTronics AskewTronics · Answer 2 · 2019-07-29T12:56:17+02:00

Answer:

Surface area of walls (38.48 meter squares)>the total surface area of 480 sheets(28.224 meter squares) .Thus the given situation is not possible .

Explanation:

Given dimensions of walls of room are

length L=3.7 m

breadth B= 3.7 m

Height H= 2.6 m

Therefore surface area [tex]S= 2H(L+B)[/tex]

=>[tex]S= 2\times 2.6(3.7+3.7)m^{2}=38.48m^{2}[/tex]

Dimensions of sheets of book

length l=0.21 m

breadth b=0.28 m

Surface area of single sheet , [tex]A=lb=0.21\times 0.28 m^{2} = 0.0588 m^{2}[/tex]

Therefore total surface area of 480 sheets of book is

[tex]A_t=480A=480\times 0.0588 m^{2}=28.224 m^{2}[/tex]

Since S> A_t surf,i.e.,ace area of walls of room is much greater than the total surface area of sheets of book, it is not possible to completely wallpaper the walls of the room with pages from his physics text .