Answer:
Part a) The length of the longest rod that can be placed in the room is 42.43 m
Part b) The total surface area is 
Part c) The volume is equal to 
Step-by-step explanation:
Part a) Find the length of the longest rod that can be placed in the room
The room is in the shape of a rectangular prism, so the longest rod that can be placed in the room is equal to the diagonal of the rectangular prism
Let
d -----> diagonal of the base of the room
D ----> diagonal of the rectangular prism
step 1
Find the diagonal of the base
Applying the Pythagoras Theorem



step 2
Find the diagonal of the rectangular prism
The legs of the diagonal of the rectangular prism are the diagonal of the base and the height of the room
Applying the Pythagoras Theorem




Part b) Find the total surface area
we know that
The total surface area of the room is equal to

where
B is the area of the base of the room
P is the perimeter of the base of the room
H is the height of the room
so
![SA=2[(30)(24)]+2[30+24](18)](https://tex.z-dn.net/?f=SA%3D2%5B%2830%29%2824%29%5D%2B2%5B30%2B24%5D%2818%29)


Part c) Find the volume
we know that
The volume of the room is equal to

where
B is the area of the base of the room
H is the height of the room
so
](https://tex.z-dn.net/?f=V%3D%5B%2830%29%2824%29%5D%2818%29)
