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Question 41446: Question
A rectangular tank has a base 60 cm by 20 cm. A solid metal pyramid with base of sides 10 cm each and height 27 cm is placed inside the tank. The tank is then filled with water until it completely covers the pyramid. If the pyramid is removed, calculate the fall in the level of water in the tank.
My teacher had given the answer as 3/4 cm or 0.75 cm. He wanted us to try to do it.
I have obtained the same answer and I don’t seem to be able to explain it. Perhaps, you can tell me what I have done is correct.
Let the fall in the level of water in the tank = h
Volume of the tank
= base x height
= 60 x 20 x h
= 1200 h
Volume of the pyramid
= 1/3 x base area x height
= 1/3 x 10 x 10 x 27
= 900
What I did was :-
Volume of the tank = Volume of the pyramid
1200h = 900
h = 900/1200
h = 3/4
I find the way I did it unexplainable. What do you think ? Please help. Thanks.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! A rectangular tank has a base 60 cm by 20 cm. A solid metal pyramid with base of sides 10 cm each and height 27 cm is placed inside the tank. The tank is then filled with water until it completely covers the pyramid. If the pyramid is removed, calculate the fall in the level of water in the tank.
My teacher had given the answer as 3/4 cm or 0.75 cm. He wanted us to try to do it.
GOOD TO SEE YOUR SINCERE ATTEMP TO SOLVE THE PROBLEM BY YOUR SELF.KEEP IT UP
SEE MY COMMENTS BELOW
I have obtained the same answer and I don’t seem to be able to explain it. Perhaps, you can tell me what I have done is correct.
Let the fall in the level of water in the tank = h
Volume of the tank
= base x height
= 60 x 20 x h
= 1200 h.,.................................OK AS A FORMULA
Volume of the pyramid
= 1/3 x base area x height
= 1/3 x 10 x 10 x 27
= 900=VP SAY...............................GOOD
What I did was :-...NO...THINK IT OVER ..PROCEED SYSTEMATICALLY AS GIVEN.WITH PYRAMID IN PLACE HE FILLED WATER TO THE TOP ..THAT IS TO THE HEIGHT OF PYAMID..THAT IS H=27 CM.SO FIRST FIND THIS VOLUME WHICH OFCOURSE INCLUDES THE VOLUME OF PYRAMID.SO.....
60*20*27=VOLUME OF PYRAMID(VP)+VOLUME OF WATER IN INTERSPACE BETWEEN PYRAMID AND TANK (VW)
32400=900+VW
VW=32400-900=31500
NOW THE PYRAMID IS REMOVED.SO WATER LEVEL DROPS LET ITS DROP=X
SO HEIGHT OF WATER IN TANK NOW =27-X
60*20*(27-X)=31500
27-X=31500/1200=26.25
X=27-26.25=0.75 CM IS THE CORRECT WORKING...LET ME QUALIFY..MATHEMATICALLY.
BUT THEN HOW DID YOU GET THE SAME ANSWER?YOU GOT IT BECAUSE KNOWINGLY OR UNKNOWINGLY YOU USED A WELL KNOWN PRINCIPLE IN PHYSICS.
IT IS CALLED ARCHIMEDES PRINCIPLE..WHICH FOR THE PURPOSE OF THIS PROBLEM CAN BE SIMPLIFIED TO STATE THAT
WHEN A SOLID (PYRAMID HERE) IS FULLY IMMERSED IN A LIQUID (WATER HERE),IT APPEARS TO LOSE SOME WEIGHT WHICH IS EQUAL TO THE WEIGHT OF LIQUID DISPLACED.
SO WE GET VOLUME OF LIQUID DISPLACED = VOLUME OF PYRAMID IMMERSED,AND WHEN YOU FOUND THE HEIGHT SUCH A VOLUME WOULD TAKE IN THE TANK ,YOU AUTOMATICALLY GOT THE DROP IN HEIGHT.SO YOUR WORKING IS ALSO CORRECT FOR PHYSICISTS.AFTER ALL YOU CANT HELP IF YOUR MATHS TEACHER DOES NOT UNDERSTAND IT!!!!
Volume of the tank = Volume of the pyramid
1200h = 900
h = 900/1200
h = 3/4
I find the way I did it unexplainable. What do you think ? Please help. Thanks.
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