Ben placed a stone in an empty rectangular tank, 50cm long and 40cm wide. He then filled the tank with water flowing from a tap at a rate of 10 liters per minute. it took 3 min to fill the tank to a depth of 18cm to cover the stone completely. Find the volume of the stone. please Help!
amount of water poured in = 3(10) = 30 litres
= 30,000 cm^3
height of water without the stone --- h cm
h(40)(50) = 30000
h = 15 cm
when the stone is included, h = 18 cm
so the difference of 3 cm must have been caused by the stone
Volume for the extra 3 cm height
= 3(40)(50) = 6000 cm^3
volume of stone = 6000cm^3
To find the volume of the stone, we need to determine the volume of water that filled the tank.
The tank has dimensions of 50cm in length, 40cm in width, and was filled to a depth of 18cm.
First, let's convert the dimensions to meters, as it is a more commonly used unit for volume:
Length: 50 cm = 0.50 m
Width: 40 cm = 0.40 m
Depth: 18 cm = 0.18 m
The volume of the tank is then calculated by multiplying the length, width, and depth:
Volume of tank = length × width × depth
= 0.50 m × 0.40 m × 0.18 m
= 0.036 m³
Next, we'll determine the volume of water that flowed into the tank during the 3-minute filling period. We know that the rate of water flow is 10 liters per minute, and we can convert this to cubic meters:
1 liter = 0.001 cubic meters
Volume of water = rate of flow × time
= 10 liters/minute × 3 minutes
= 30 liters
= 0.030 cubic meters
Finally, to find the volume of the stone, we subtract the volume of water from the volume of the tank:
Volume of stone = Volume of tank - Volume of water
= 0.036 m³ - 0.030 m³
= 0.006 m³
Therefore, the volume of the stone is 0.006 cubic meters.
To find the volume of the stone, we need to calculate the volume of water that flowed into the tank while submerging the stone.
First, let's calculate the volume of water that flowed into the tank in 3 minutes. We know that the rate at which water flows from the tap is 10 liters per minute. So, in 3 minutes, the volume of water that flowed into the tank is 10 liters/minute * 3 minutes = 30 liters.
Now, let's calculate the volume of water that covered the stone. The tank's dimensions are 50 cm (length) * 40 cm (width) * 18 cm (depth) = 36,000 cm³. However, we need to convert this volume to liters because we measured the water flow rate in liters. Since 1 liter is equal to 1000 cm³, the volume in liters is 36,000 cm³ / 1000 = 36 liters.
The difference in volume between the water that filled the tank (30 liters) and the volume of water that covered the stone (36 liters) gives us the volume of the stone.
Stone's Volume = Volume of water that filled the tank - Volume of water that covered the stone
Stone's Volume = 36 liters - 30 liters = 6 liters
Therefore, the volume of the stone is 6 liters.