• anonymous
An empty rectangular tank, 40 cm long and 25 cm wide, contains 2 metal cubes of edge 10 cm. the tank is being filled with water flowing from a tap at a rate of 10 liters per minute. If it takes 3 minutes to fill up the tank, find the height of the tank.
  • Stacey Warren - Expert
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  • chestercat
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  • anonymous
Ok, there are many things to this question so you should be careful first things first, the volume of the water that can fill the tank is equal to the volume that the tank has inside, and the volume that the tank has inside is equal to the volume of the tank minus the volume of the 2 cubes \[V_{water}=V_{cuboid}-(2 \times V_{cube})\] You can easily calculate the volume of the cube \[V_{cube}=side \times side \times side=(side)^3\] In 1 minute, 10 litres of water flow in the cuboid so in 3 minutes, 3 times 10 or 30 litres of water will flow into the cuboid \[\implies V_{water}=3 \times 10 = 30\] remember this volume is in litres and u need to convert it into cubic meter the volume of cuboid can also be easily calculated as \[V_{cuboid}=length \times breadth \times height\] Using all this information put the values in the first equation I gave to solve for height

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