SOLUTION: the base of a container is a square of side 30 cm. a stone is placed in the container. then water is poured into the container until it is 3/4 full. when the stone is removed, the

Algebra ->  Volume -> SOLUTION: the base of a container is a square of side 30 cm. a stone is placed in the container. then water is poured into the container until it is 3/4 full. when the stone is removed, the       Log On


   

Question 965680: the base of a container is a square of side 30 cm. a stone is placed in the container. then water is poured into the container until it is 3/4 full. when the stone is removed, the water level drops to 5/8 of the height of the container. if the volume of the stone is 4500 cubed cm, find the height of the container.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
When the stone is removed, occupied tank volume changes from 3/4 full to 5/8 full;
when 4500 cm^3 is removed, the tank filled volume changes from 6/8 full to 5/8 full;

When 4500%2Acm%5E3 is removed, the was a tank volume change of 6%2F8-5%2F8=1%2F8 of the tank's volume.

The tank volume is proportional to its height or tallness.
30%2A30%2Ay=4500, using y for the amount of vertical length along the tank for the stone.

y=4500%2F900
y=45%2F9
y=5, this is centimeters.

That y=5 is %281%2F6%29 of the tank's height.


Finally, if h is the actual tank height

highlight_green%28y%2Fh=1%2F6%29

y=h%2F6

6%2Ay=h

h=6%2Ay

h=6%2A5

highlight%28h=30%2Acentimeters%29