Answer :
Final answer:
To find the maximum length of the room that can be cooled by an air conditioner with a capacity of 3,600 cubic feet, we divide the total volume by the product of the given width and height of the room. This results in a maximum room length of 24 feet.
Explanation:
To calculate the greatest length the room can have and still be cooled by the air conditioner, we use the volume of the room that the air conditioner can cool, which is 3,600 cubic feet. Given that the room is a rectangular prism 15 feet wide and 10 feet tall, we can use the formula for the volume of a rectangular prism: Volume = length × width × height. Here we have the width (15 feet) and height (10 feet), and we need to find the maximum length. Since the air conditioner can cool a room with a volume of up to 3,600 cubic feet, we set up the equation:
3,600 = length × 15 × 10
Now we solve for length:
3,600 = 150 × length
length = 3,600 ÷ 150
length = 24 feet
Therefore, the greatest length the room can be to be cooled by the air conditioner is 24 feet.
