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i) Which box has the greater lateral surface area and by how much?

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

Answer :

Given:

Edge of cube = 10 cm

Length (l) of box = 12.5 cm

Breadth (b) of box = 10 cm

Height (h) of box = 8 cm

i) We know that, Lateral surface area of cubical box

= \(4 × (Edge)^2\)

= \(4 × (10)^2 {cm}^2\)

= 400 \({cm}^2\)

Also, We have,

Lateral surface area of cuboidal box

= 2 [lh + bh]

= [2 (12.5 x 10 x 8)] \({cm}^2\)

= [2 x 180] \({cm}^2\)

= 360 \({cm}^2\)

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

Now, Lateral surface area of cubical box - Lateral surface area of cuboidal box

= 400 \({cm}^2\) - 360 \({cm}^2\) = 40 \({cm}^2\)

Therefore, the lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box by 40 \({cm}^2\)

ii)Similarly, Total surface area of cubical box

=\(6 × (Edge)^2\)

= \(6 × (10)^2 {cm}^2\)

= 600 \({cm}^2\)

Also, We have,

Total surface area of cuboidal box

= 2(lh + bh + lb)

=[2 (12.5 x 8 + 10 x 8 + 12.5 x 100)] \({cm}^2\)

= 610 \({cm}^2\)

Clearly, the total surface area of the cubical box is smaller than that of the cuboidal box.

Now, Total surface area of cuboidal box - Total surface area of cubical box

= 610 \({cm}^2\) - 600\({cm}^2\)

= 10 \({cm}^2\)

Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 \({cm}^2\).

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