The area of the carpet with dimensions 6 ft by 10 ft is 60 ft^2.

The cost per ft^2 is: 400/60 = $20/3 per ft^2

We need to find the cost of carpet with dimensions 18 ft by 30 ft.

First we will find the area: 18*30 = 540 ft^2

Then we multiply the area with the cost per ft^2:

540*(20/3) = $3,600

The cost of the carpet for a room 18 by 30 ft is $3,600.