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01 Jun 2022, 07:30
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48% (01:55) correct
52%
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wrong
based on 25
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A certain cylindrical tank set on its circular base is 7.5 feet in height. If the tank is filled with water, and if the water is then poured out of the tank into smaller cube-shaped tanks, how many cube-shaped tanks are required to hold all the water?
(1) The length of a cube-shaped tank’s side is equal to the radius of the cylindrical tank’s circular base.
(2) If three cube-shaped tanks are stacked on top of one another, the top of the third cube stacked is the same distance above the ground as the top of the cylindrical tank.
(1) The length of a cube-shaped tank’s side is equal to the radius of the cylindrical tank’s circular base.
(2) If three cube-shaped tanks are stacked on top of one another, the top of the third cube stacked is the same distance above the ground as the top of the cylindrical tank.
01 Jun 2022, 08:11
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IMO C
A certain cylindrical tank set on its circular base is 7.5 feet in height. If the tank is filled with water, and if the water is then poured out of the tank into smaller cube-shaped tanks, how many cube-shaped tanks are required to hold all the water?
(1) The length of a cube-shaped tank’s side is equal to the radius of the cylindrical tank’s circular base.
(2) If three cube-shaped tanks are stacked on top of one another, the top of the third cube stacked is the same distance above the ground as the top of the cylindrical tank.
To answer this question we need to have 2 things , the radius of the base of the circle (R) and length of any side of the cube (L)
From Statement one :
The length of a cube-shaped tank’s side is equal to the radius of the cylindrical tank’s circular base.
=> R=L
volume of cylinder = πR^2H= πL^2H
and if X number of cubes can be filled with the same volume of water
\(XL^3 = πL^2H\)
\(XL = πH\)
\(XL= \frac{22}{7} * 7.5-\)-> this gives us a relationship between L and H (INSUFF)
From Statement two :
3L=H , where H= 7.5
so L = 2.5 --> we have length of cube but we do not know about the radius of cylinder form this statement (INSUFF)
Combining both :
if L=2.5
\(X* 2.5 = \frac{22}{7} *7.5\)
this gives us the value of X.
A certain cylindrical tank set on its circular base is 7.5 feet in height. If the tank is filled with water, and if the water is then poured out of the tank into smaller cube-shaped tanks, how many cube-shaped tanks are required to hold all the water?
(1) The length of a cube-shaped tank’s side is equal to the radius of the cylindrical tank’s circular base.
(2) If three cube-shaped tanks are stacked on top of one another, the top of the third cube stacked is the same distance above the ground as the top of the cylindrical tank.
To answer this question we need to have 2 things , the radius of the base of the circle (R) and length of any side of the cube (L)
From Statement one :
The length of a cube-shaped tank’s side is equal to the radius of the cylindrical tank’s circular base.
=> R=L
volume of cylinder = πR^2H= πL^2H
and if X number of cubes can be filled with the same volume of water
\(XL^3 = πL^2H\)
\(XL = πH\)
\(XL= \frac{22}{7} * 7.5-\)-> this gives us a relationship between L and H (INSUFF)
From Statement two :
3L=H , where H= 7.5
so L = 2.5 --> we have length of cube but we do not know about the radius of cylinder form this statement (INSUFF)
Combining both :
if L=2.5
\(X* 2.5 = \frac{22}{7} *7.5\)
this gives us the value of X.
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