# A solid cube is cut into two cuboid of equal volumes . find the ratio of the total surface area of the given cube and that of one of the cuboids.

Solution :  Let the edge of the solide cube be a units. Since the cube is cut into two cuboids of equql volumes .

Therefore , the dimensions of each of the cuboid are  length  = a units , breadth  = a units and  height = a/2 units .

Now ,      S = Total surface area of cube $=6a^2 sq. units$

$S_{1}$ = Total surface area of one cuboid = $2\left ( a \times a +a \times \frac{a}{2 } +\frac{a}{2 }\times a\right )=4a^2sq.units$

$\therefore$           Required ratio = $S:S_{1}=6a^2:4a^2=3:2$

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