Question 1201743
<br>
I think we can call the "3000 cm^2" in the problem a typographical error instead of a fatal flaw.  Obviously the intent was 3000 cm^3....<br>
The height is 30cm, and initially the tank is 1/3 full, so it is filled to a depth of 10cm.<br>
When 3000 cm^3 of water is added, the depth of water in the tank becomes 25cm, a change of 15cm.  Since the change in the depth of the water is half the height of the tank, the 3000 cm^3 that was added is half the volume of the tank.  So the volume of the tank is 6000 cm^3.<br>
1) How much more water is needed to fill the tank to its brim?<br>
The water is now 5cm from the top of the tank.  Since adding 3000 cm^3 raised the depth of the water by 15cm, the additional amount of water needed to raise the depth of the water another 5cm is one-third of 3000 cm^3, or 1000 cm^3.<br>
ANSWER: 1000 cm^3<br>
2) what is the length of the container?<br>
The volume of the tank is 6000 cm^3, and the height is 30cm; that means the area of the rectangular base is 200 cm^2.  Then, since the length is twice the width, the length of the base is 20cm and the width is 10cm.<br>
ANSWER: 20cm<br>