Question

When a metal cube is completely submerged in water contained in a cylindrical
vessel with diameter 30 cm, the level of water rises by 1
cm. Find:
(i) the length of the edge of the cube,
(ii) the total surface area of the cube.
99​

Answer 1

Answer:

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

And when cube submerged water level increase by 14199cm  = 99 + 4199 = 14099cm

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

Volume of given cube  =  x3

We know volume of cylinder  = π r2 h , So

Volume of water  = 227 × 152 × 14099 = 2 × 15 × 15× 209 =  2 × 5 × 5×20 =  1000 cm3

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 )

Hope this information will clear your doubts about Surface Areas and Volumes .

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards