A cubical box has each edge $10 c m$ and another cubical box is $12.5 c m$ long, $10 c m$ wide and $8 c m$ high.
Which box has the smaller total surface area(in sq.cm) and by how much ?

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Solution

Cubical box: Length of the side $= a = 10$ cm

Total surface area of the cube $= 6 \times a^{2} = 6 \times 10^{2} = 600$ sq.cm

Cuboidal box:Length $= l = 12.5$ cm, Breadth $= b = 10$ cm and height $= h = 8$ cm

Total surface area of the cuboid $= 2 (l b + b h + l h)$
$= 2 (12.5 \times 10 + 10 \times 8 + 12.5 \times 8) = 2 (125 + 80 + 100) = 610 ‬$ sq.cm

$∴$ Total surface area of the cuboid $>$ Total surface area of the cube by $= 610 - 600 = 10$ sq.cm

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A cubical box has each edge $10 c m$ and another cuboidal box is $12.5 c m$ long, $10 c m$ wide and $8 c m$ high.

(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?

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long ,10 cm wide,and 8 cm high.

1.which box has the greater lateral surface area and by how much?

2.which box has the smaller total surface area and by how much?

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