A rectangular tank 25 cm long and 20 cm wide contains 4.5 litres of water. When a metal cube is lowered in the tank, the water level rises to height of 11 cm. Find the length of edge of the cube ?

15

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Solution

The correct option is D $10$ cm
The tank is in the shape of a cuboid.
Since the tank contains $4.5$ litres of water, its volume is $4.5 \times 1000 {c m}^{3} = 4500 {c m}^{3}$
Volume of a cuboid of length l, breadth b and height h $= l \times b \times h$
Hence, $25 \times 20 \times h = 4500$
$h = 9 c m$
Hence, height of the water in tank is $9 c m$
Increase in level of water in the tank after the cube is dropped $= 11 - 9 = 2 c m$
Volume of cube $=$ volume of water displaced $= 25 c m \times 20 c m \times 2 c m = 1000 {c m}^{3}$
Volume of a cube $= {s i d e}^{3}$
Length of each side of the cube $= \sqrt[3]{1000} = 10 c m$

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