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A cuboidal fish tank having l,b,h as 60 cm, 40 cm & 80 cm respectively is filled with water. The base of the tank is tilted by 45 degrees along the breadth & water coming out from the tank is collected in an empty vessel. Volume of the water collected in the vessel is 32 litres. Determine the height of water that was initially there in the tank. (Assume thickness of tank to be negligible) A) 80 cm B) 60 cm C) 63.33 cm D) 76.66 cm
Once the cuboid is tilted, the empty space will be in the form of a right angled triangle with sides equal to 60 cm. So area of cross section will be 1/2*60*60. The breadth is 40 cm, so volume is 1/2*60*60*40
After the tank is tilted, the volume of empty space in the tank equals 1/2*60*60*40 = 72 litres.
This includes 32 litres of water which was collected.
So, the volume of the empty space before was 40 litres.
Hence, the height of the empty space was 40*1000/(40*60) = 16.66 cm
Hence, the height of water originally was 80-16.66 = 63.33 cm
Answer is c
