# 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.(ii) Which box has the smaller total surface area and by how much?

N Nehul

Given,

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

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

(ii) The total surface area of the cubical box = $6\times(10\times10)\ cm^2 = 600\ cm^2$

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

$\\ = [2(12.5 � 8 + 10 � 8 + 12.5\times10)]\ cm^2 \\ = 610\ cm^2$

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

Difference between them = $610-600 = 10\ cm^2$

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