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A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (i) Which box has the greater lateral surface area and by how much?

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?

 

Answers (1)
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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

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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