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A solid cube is cut into two cuboids exactly at the middle as shown in figure. Find the ratio of total surface area of the given cube and that of the cuboid.

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3 : 2

2 : 5

5 : 7

6 : 1

answer is A.

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Detailed Solution

Cube’s overall surface area,

= 6 l^{2}

Here, l is the side of cube.
When, cube is divided into two cuboids from the centre, then the width of new figure,

= \frac{l}{2}

. Here height and length remain same and equals to l.
So, the total surface area of new cuboid formed is,

\Rightarrow 2 (lb + b h + l h) c m^{2}

\Rightarrow 2 (l \times \frac{l}{2} + \frac{l}{2} \times l + l \times l) c m^{2}

\Rightarrow 2 (\frac{l^{2}}{2} + \frac{l^{2}}{2} + l^{2}) c m^{2}

\Rightarrow 2 (\frac{l^{2} + l^{2} + 2 l^{2}}{2}) c m^{2}

\Rightarrow 2 (\frac{4 l^{2}}{2}) c m^{2}

\Rightarrow 4 l^{2} c m^{2}

So, the ratio of surface area,

= \frac{6 l^{2}}{4 l^{2}}

= 3 : 2

Hence the option 1 is correct.

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