QuestionA tank is long, wide, with 3 cubes of edge . It fills at 10 L/min for 6 min. Find height.
Studdy Solution
STEP 1
Assumptions1. The tank is rectangular in shape with length60 cm and width50 cm.
. The tank contains3 metal cubes each with an edge of10 cm.
3. The tank is being filled with water flowing from a tap at a rate of10 liters per minute.
4. It takes6 minutes to fill up the tank.
5. The tank is filled up to its brim.
STEP 2
First, we need to find the volume of water that fills the tank. We can do this by multiplying the rate of water flow by the time it takes to fill the tank.
STEP 3
Now, plug in the given values for the flow rate and time to calculate the volume of water.
STEP 4
Calculate the volume of water that fills the tank.
STEP 5
We know that1 liter equals1000 cubic centimeters. So, we need to convert the volume of water from liters to cubic centimeters.
STEP 6
Calculate the volume of water in cubic centimeters.
STEP 7
The volume of water that fills the tank is equal to the volume of the tank minus the volume of the3 cubes. So, we need to find the volume of one cube and then multiply it by3.
STEP 8
Plug in the given value for the edge to calculate the volume of one cube.
STEP 9
Calculate the volume of one cube.
STEP 10
Calculate the total volume of the3 cubes.
STEP 11
The volume of the tank is equal to the volume of the water plus the volume of the cubes. So, we can find the volume of the tank.
STEP 12
Plug in the values for the volume of water and the volume of the cubes to calculate the volume of the tank.
Volume_{tank} =60000\, cm^ +3000\, cm^
STEP 13
Calculate the volume of the tank.
STEP 14
The volume of a rectangular tank is given by the product of its length, width, and height. So, we can find the height of the tank by dividing the volume of the tank by the product of its length and width.
STEP 15
Plug in the values for the volume of the tank, length, and width to calculate the height of the tank.
STEP 16
Calculate the height of the tank.
The height of the tank is21 cm.
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