Rain water from the flatt roof of a building 20 m by 5 m
flows into a cylindrical tank of diameter 2 m.
Find the increase in depth of water in the tank
after 11 mm of rain.
Give your answer in meters.
Vcyulinder= Πr2h. Use Π≈(22/7).
no idea, unless you say how fast it's raining.
To find the increase in depth of water in the tank, we need to determine the volume of water that flows into the tank due to the rainfall.
First, let's calculate the volume of rainwater that falls on the entire roof. The area of the roof is given as 20 m by 5 m, so the total area is 20 * 5 = 100 square meters.
Next, we need to find the volume of rainwater that falls on the roof. The given rainfall is 11 mm, which means that for every square millimeter of the roof, 11 cubic millimeters of rainwater falls.
To convert this into cubic meters, we need to divide the rainfall by 1,000,000 since there are 1,000,000 square millimeters in a square meter. So, the volume of rainwater falling on the roof is (100 * 11) / 1,000,000 = 11/1000 cubic meters.
Now, let's calculate the volume of the cylindrical tank. The formula for the volume of a cylinder is V_cylinder = πr^2h, where r is the radius and h is the height. We are given that the diameter of the tank is 2 m, which means the radius is 2/2 = 1 m.
Plugging these values into the formula, we get V_cylinder = (22/7) * 1^2 * h = (22/7)h cubic meters.
To find the increase in depth of water in the tank, we need to subtract the initial volume of water in the tank from the final volume of water after the rainfall. The initial volume of water can be assumed to be zero since the tank is empty.
Therefore, the increase in depth of water in the tank is equal to the volume of rainwater, which is 11/1000 cubic meters.
So, the increase in depth of water in the tank is 11/1000 meters or 0.011 meters (rounded to three decimal places).
Therefore, the increase in depth of water in the tank after 11 mm of rain is 0.011 meters.