Question

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10
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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Answer 1

(i) Lateral surface area of cubical box = 4a2 = 4 x 102 = 400 cm2

Lateral surface area of cuboidal box = 2h (l + b)

= 2 x 8(12.5 +10) = 16 X 22.5 = 360 cm2

Thus, lateral surface area of cubical box is greater by

(400 cm2 - 360 cm2) = 40 cm2

(ii) Total surface area of cubical box = 6a2 = 6 x 102 cm2 = 600 cm2

Total surface area of cuboidal box = 2 (lb + bh + hl)

= 2(12.5 x 10 + 10 x 8 + 8 x 12.5)

= 2(125 + 80 + 100) = 2 x 305cm2 = 610 cm2

Thus, total surface area of cuboidal box is greater by (610 - 600) cm2

= 10 cm2