Q. 54.3( 376 Votes )

# 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?

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

Answer :

(i) Edge of cube = 10 cm

Length (l) of box = 12.5 cm

Breadth (b) of box = 10 cm

Height (h) of box = 8 cm

Lateral surface area (Cubical box) = 4(edge)^{2}

= 4(10 cm)^{2}

= 400 cm^{2}

Lateral surface area (Cuboidal box) = 2[lh + bh]

= [2(12.5 × 8 + 10 × 8)] cm^{2}

= (2 × 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

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) Total surface area of cubical box = 6(edge)^{2}

= 6(10 cm)^{2}

= 600 cm^{2}

Total surface area of cuboidal box = 2[lh + bh + lb]

= [2(12.5 × 8 + 10 × 8 + 12.5 × 10] cm^{2}

= 610 cm^{2}

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

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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