Q : 5      A cubical box has each edge $\small 10 \hspace{1mm}cm$ and another cuboidal box is $\small 12.5 \hspace{1mm}cm$ long, $\small 10 \hspace{1mm}cm$ wide and $\small 8 \hspace{1mm}cm$ high.             (i) Which box has the greater lateral surface area and by how much?

Given,

Edge of the cubical box = $\small 10 \hspace{1mm}cm$

Dimensions of the cuboid = $12.5\cm \times 10\ cm \times 8\ cm$

The lateral surface area of the cubical box = $4\times(10\times10)\ cm^2 = 400\ cm^2$

The lateral surface area of the cuboidal box = $2[lh + bh]$

$\\ = [2(12.5 � 8 + 10 � 8)]\ cm^2 \\ = (2 \times 180)\ cm^2 \\ = 360\ cm^2$

Clearly, Lateral surface area of the cubical box is greater than the cuboidal box.

Difference between them = $400-360 = 40\ cm^2$

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