when a metal cube is completely submerged in a cylindrical vessel containing water with diameter 30 cm, the level of water rises by 1 whole 41 over 99 cm, find length of edge of the cube and T.S.A of the cube ? ( urgent ans pls )

Dear Student,

Please find below the solution to the asked query:

Given : Diameter of cylindrical vessel  =  30 cm , So radius  = 15 cm 

And when cube submerged water level increase by $1\frac{41}{99}\mathrm{cm} = \frac{99 + 41}{99} = \frac{\mathbf{140}}{\mathbf{99}}\mathbf{cm}$

Let edge of cube  = x  and we know volume of cube  = ( Edge )³ , So

Volume of given cube  =  x³


We know volume of cylinder  = $\mathrm{\pi } r^2 h$ , So

Volume of water  = $\frac{22}{7} \times {15}^2 \times \frac{140}{99} = 2 \times 15 \times 15\times \frac{20}{9} = 2 \times 5 \times 5\times 20 = \mathbf{1000}\mathbf{ }{\mathbf{cm}}^{\mathbf{3}}$
Here , when a cube is submerged into a cylindrical vessel, the volume of water displaced is equal to the volume of cube .

Therefore,

x³ =  1000

x³ = 10³

x  =  10 

So,

Edge of cube  =  10 cm                                                        (  Ans )

We know Total surface area of cube  = 6 ( Edge )²

So,
Total surface area of given cube  = 6 ( 10)² =  6 ( 100 ) = 600 cm²                                            ( Ans )


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