<p>A rectangular tank has a length of 3 feet, a width of 4 feet, and a height of 5 feet. The tank is half filled with water. If a metal cube with sides that are 1 foot long is submerged in the water, by how many INCHES will the level of the water rise?</p>
<p>A) 1
B) 2
C) 4
D) 6
E) 12</p>
<p>The answer is A) 1 inch.</p>
<p>Please explain why? I chose E) 12.</p>
<p>This is strange… this is more of science than math…</p>
<p>volume of metal cube with sides that are 1 foot long = 1 cubic ft.</p>
<p>The level increase of water = the volume of the object.</p>
<p>Yeah but the question asks how many INCHES not FEET, so I’m confused as to why the answer should be 1 INCH.</p>
<p>Volume of tank = 3<em>4</em>5 = 60
Tank is half filled so there is 30 cubic feet of water
height of water is 2.5ft
Volume of cube = 1^3 = 1
height of cube is 1 ft, so volume of water in first foot is displaced by 1.
New volume for first foot of water = (3<em>4</em>1)-1 = 11
That leaves 19 cubic feet of water left
19 = 3<em>4</em>h
h = 19/12
total height of water is 19/12 +1 = 31/12
Subtract 2.5 or 30/12
31/12 - 30/12 = 1/12
water rose 1/12 feet or 1 inch</p>
<p>Thanks Lambda, but how did you know to do the step where you find the new volume of the first foot of water? I chose 12 inches originally because I thought that the level increase of water is equal to the volume of the object placed in?</p>
<p>Once you know the whole cube was submerged, the half filled with water and the 5’ height become secondary (it would only have mattered if the cube caused water to spill out).</p>
<p>The volume of themetal cube is 1 cu ft. The surface area of the tank is 3’ x 4’. Assuming h is the height of the displaced water, the equation hecomes:
3 x 4 x h = 1 x 1 x 1, ie. h = 1/12’ or an inch.</p>