a flat rectangualar roof is 20m long and 12m wide. All rain falling on the roof drains into a closed cylindrical water tank. If 1cm of rain falls on the roof find
a)how many litres of water drain into the tank
Working out shown please
So you want the volume of a "box" which is
20 m by 12 m by 1 cm
or
2000 cm by 1200 cm by 1 cm
= ...... cm^3
and if 1 L = 1000 cm^3 ...... ?????
To determine the number of liters of water that drains into the tank, we need to find the volume of the water that falls on the roof.
Step 1: Calculate the area of the roof
The area of a rectangle is given by the formula A = length x width.
In this case, the length of the roof is 20m and the width is 12m. Therefore, the area of the roof is:
A = 20m x 12m = 240 square meters.
Step 2: Convert the rain depth into meters
Given that 1cm of rain falls on the roof, we need to convert it into meters before calculating the volume. Since 1 meter is equivalent to 100 centimeters, we can divide 1cm by 100 to get the rain depth in meters.
Rain depth = 1cm / 100 = 0.01m.
Step 3: Calculate the volume of water
The volume of water is given by the formula V = area x depth.
In this case, the area is 240 square meters (from step 1) and the rain depth is 0.01m (from step 2). Therefore, the volume of water that drains into the tank is:
V = 240m^2 x 0.01m = 2.4 cubic meters.
Step 4: Convert the volume into liters
Since 1 cubic meter is equivalent to 1000 liters, we can multiply the volume by 1000 to convert it into liters.
Volume in liters = 2.4 cubic meters x 1000 = 2400 liters.
Therefore, if 1cm of rain falls on the flat rectangular roof, approximately 2400 liters of water will drain into the closed cylindrical water tank.