Question

Question: Which of the following could be the possible dimensions of a room with an air volume of 1440 cubic feet?

• A. $l=18ft,w=10ft,h=8ft$
• B. All of the above
  
• C. $l=12ft,w=15ft,h=8ft$
• D. $l=12ft,w=12ft,h=10ft$

Answer 1

The correct option is B All of the above


$l=18ft,w=10ft,h=8ft$
Volume of the room $=l\times w\times h$ (Since the room is a rectangular prism.)
$=18\times 10\times 8$
$=180\times 8$
$=$ 1440 cu ft
Since the volume for the given dimensions is the same as 1440 cu ft, these could be the dimensions of the room.

Option b:$l=12ft,w=12ft,h=10ft$
Volume of the room $=l\times w\times h$ (Since the room is a rectangular prism.)
$=12\times 12\times 10$
$=144\times 10$
$=$ 1440 cu ft
Since the volume for the given dimensions is the same as 1440 cu ft, these could be the dimensions of the room.

Option c: $l=12ft,w=15ft,h=8ft$
Volume of the room $=l\times w\times h$ (Since the room is a rectangular prism.)
$=12\times 15\times 8$
$=180\times 8$
$=1440$ cu ft
Since the volume for the given dimensions is same as 1440 cu ft, these could be the dimensions of the room

Therefore, the volume of the room for all the given dimensions is equal to 1440 cubic ft.