A storage tank is in the form of a cube . When it is full of water, the volume of water is `15.625 m^(3)`. If the present depth of water is `1.3 m,` then, find the volume of water already used from the tank.

Explanation

Let each edge of the tank be `a` metres.
Volume of water in the tank when it is full `= (a^(3)) m^(3)`
But, volume of water in full tank `= 15.625 m^(3)`
`:. a^(3) = 15.625 = (15625)/(1000) = (125)/(8) = ((5)/(2))^(3)`
`rArr a = (5)/(2) = 2.5`
Thus, each edge of the tank is 2.5 m
Present depth of water = 1.3 m
Present volume of water in the tank
`= (2.5 xx 2.5 xx 1.3) m^(3)`
`= ((5)/(2) xx (5)/(2) xx (13)/(10)) m^(3) = (65)/(8) m^(3) = 8.125 m^(3)`
Volume of water used from the tank
`= (15.625 - 8.125) m^(3) = 7.5 m^(3)`