A rectangular container 45cm long and 25cm wide was full of water. After removing 22.5 liters of the water, the level of water became 4cm high. What was the height of the container?
let the height be x cm
original volume = (45)(25)x cm^3 = 1125x cm^3
remember 1L = 1000 cm^3 (the beauty of the metric system)
volume removed = (45)(25)(x-4)
which is 22500
1125(x-4) = 22500
1125x - 4500 = 22500
1125x = 27000
x = 24
the height was 24 cm
Mathematics question
20cm
I'm sorry, I need more information about the question to provide an answer. Could you please give me the full question?
To determine the height of the container, we need to first find the volume of water that was removed, and then calculate the original height using that information.
The formula for calculating the volume of a rectangular container is:
Volume = Length * Width * Height
Given:
Length = 45 cm
Width = 25 cm
Let's find the original volume of the water:
Original Volume = 45 cm * 25 cm * Height (cm)
Now, we also know that 22.5 liters of water were removed. To convert liters to cubic centimeters, we use the conversion factor:
1 liter = 1000 cubic centimeters
So, the volume of water that was removed can be calculated as:
Volume Removed = 22.5 liters * 1000 cubic centimeters/liter
Now, we can rewrite the equation to solve for the height of the container:
Original Volume - Volume Removed = Length * Width * Height
45 cm * 25 cm * Height - (22.5 liters * 1000 cubic centimeters/liter) = 0 (since all the water was removed)
Simplifying the equation:
1125 cm^2 * Height - 22500 cm^3 = 0
Rearranging the equation to solve for the height:
1125 cm^2 * Height = 22500 cm^3
Height = 22500 cm^3 / 1125 cm^2
Height = 20 cm
Therefore, the height of the container is 20 cm.