The cross section of a rectangular tank measures 1.2m by 0.9m,it contains water of a debt 0.4m if a cubic block of Sides 50cm is lowered into tank cal to 2 s.f the use in the water level in meters?
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The space it occupied is filled by fluid having a weight wfl. This weight is supported by the surrounding fluid, and so the buoyant force must equal wfl, the weight of the fluid displaced by the object. It is a tribute to the genius of the Greek mathematician and inventor Archimedes (ca. 287–212 B.C.) that he stated this principle long before concepts of force were well established. Stated in words, Archimedes’ principle is as follows: The buoyant force on an object equals the weight of the fluid it displaces. In equation form, Archimedes’ principle is
FB = wfl,
where FB is the buoyant force and wfl is the weight of the fluid displaced by the object. Archimedes’ principle is valid in general, for any object in any fluid, whether partially or totally submerged.
ARCHIMEDES’ PRINCIPLE
According to this principle the buoyant force on an object equals the weight of the fluid it displaces. In equation form, Archimedes’ principle is
FB = wfl,
where FB is the buoyant force and wfl is the weight of the fluid displaced by the object.
The first image below is a sketch of the cuboidal tank containing the shaded portion of water with an assumed height postion attached to its side.
The second image shows a predicted but imagined height of the water after a cubic block was inserted. You can also see a change in water level on the right hand side of that sketch.
The third image reveals the analyses of the problem. In this scheme, the volume of a cuboid and cube are noted. Then, each of them is used to calculate the possible volume of either the cuboidal tank or cubic block with respect to the given parameters from the question.
NB: The side of the cubic block is in centimetre, so it needs to be converted to metre format to suit the progress of the calculation. Either cm or m can be worked with, but the working was done as regards m. Thus, the final answer would be in m³.
In addition, the total volume after the insertion of that block must be determined before a new height can be obtained from the usage of the same cuboidal formula for its volume.
This fourth image below is a calculation of the new height of the water in the tank and the possible change in the its level. Th answer there is in 3 s.f. However, in 2, the result would be 0.13m.
