maths question please answer this

Question

An aquarium has a rectangular base that measures $100$ cm by $40$ cm and has a height of $50$ cm. The aquarium is filled with water to a depth of $37$ cm. A rock with volume $1000\text{cm}^3$ is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?

idk really understand this stuff so please explain it with details I know the answer (0.25) but I don't understand how 

I have exam tomorrow 

Answer 1

“Let's begin with the story: the local tyrant contracts the ancient Greek polymath Archimedes to detect fraud in the manufacture of a golden crown. Said tyrant, name of Hiero, suspects his goldsmith of leaving out some measure of gold and replacing it with silver in a wreath dedicated to the gods. Archimedes accepts the challenge and, during a subsequent trip to the public baths, realizes that the more his body sinks into the water, the more water is displaced--making the displaced water an exact measure of his volume. Because gold weighs more than silver, he reasons that a crown mixed with silver would have to be bulkier to reach the same weight as one composed only of gold; therefore it would displace more water than its pure gold counterpart. Realizing he has hit upon a solution, the young Greek math whiz leaps out of the bath and rushes home naked crying "Eureka! Eureka!" Or, translated: "I've found it! I've found it!" – Scientific American

The volume of the water [ (area of base) * (height of water) ] increases by exactly the volume of the rock ! [note: this not the weight, but the volume]

The initial volume of the water is: 100 cm * 40 cm * 37 cm = 148000 cm³

 

The final volume (water plus rock) is 148000+1000 cm³ = 149000 cm³

 

The initial height of the water was 37 cm. [that is, 148000/(100*40)]

 

The final height of the water is: 149000 cm³ / 4000 cm² = 37.25 cm

 

The water rose from 37 cm to 37.25 cm. That’s 0.25 cm.

 

To check (very important):
The water rose 0.25 cm. The volume increased 100*40*0.25 = 1000 cm
       From 148000 to 149000 cm3.     Check!

Answer 2

Volume=length*width*height

V=lwh

V=100*40*50

V=200,000 cm³ capacity

the depth or height is 50 cm

therefore each cm of depth holds 200,000/50=4000 cm³ of volume (area of base=100*40=4000 also)

every 4000 cm³ of water (or something like a rock) placed into the aquarium raises the water already inside by 1 cm

you put in a rock with a volume of 1000 cm³

the water level is raised by 1000/4000=1/4=0.25 cm (answer)

if the rock had a volume of 4000 cm³ then the water would have risen 1cm

 

Answer 3

The water level rises so that the volume of the rising water equals the volume of the rock.

r represents the amount of rise

(100cm)(40cm)(rcm) = 1000cm³

4000rcm³ = 1000cm³

rcm³ = 0.25cm³

rcm = 0.25cm