If water is poured at a rate of 12 cubic meters per second into a half-empty rectangular tank with length 5 meters, width 3 meters, and height 25 meters, then how high, in meter, will the water level be after 9 seconds ?

Options

A. `6.0`
B. `7.2`
C. `18.5`
D. `19.7`

Answer

D

Explanation

Sketch (or visualize) the situation. Before more water is added, the water level is half of 25, or 12.5 meters :

As water is poured in, the rectangular solid that represents the water gets taller, while the dimensions of the base stay the same. As water is poured in for 9 seconds at the rate of 12 cubic meters per second, the amount added is `9xx12=108` cubic meters. With a base of 3 meters by 5 meters and the 108 cubic meters of added volume, you can figure out what the added depth is :
Added volume = length `xx` Width `xx` added depth
`108=5xx3xx` added depth
added depth `= (108)/(15)=7.2`
That's on top of the pre-existing 12.5 meters. The new water level is `12.5+7.2=19.7` meters.