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?

Answers (1)

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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