Question

A cubical box has each edge 13cm and another cuboidal box 20 cm long, 15.5 cm wide and 10 cm high. (a) Which box has the greater lateral surface area and by how much? (b) Which box has the smallest total surface area and by how much?

Answer 1

Step-by-step explanation:

Cubical box :|

$edge \: (a) = 13cm$

$lateral \: surface \: area = 4 {a}^{2} = 4 \times {13}^{2} = 4 \times 169 = 676 {cm}^{2}$

$and \: total \: surface \: area = 6 {a}^{2} = 6 \times 169 = 1014 {cm}^{2}$

In Cuboid box:

$l = 20cm \: \: \: b = 15.5cm \: \: \: h = 10cm$

$lateral \: surface \: area = 2(l \times h + b \times h) = 2(20 \times 10 + 15.5 \times 10) = 2(200 + 155) = 2 \times 355 = 710 {cm}^{2}$

$and \: total \: surface \: area = 2(lb + bh + lh) = 710 + 2 \times 20 \times 15.5 = 710 + 620 = 1330 {cm}^{2}$

a) Cuboid has greater lateral surface area.

b) cube has smallest total surface area.

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Answer 2

Answer:

a) cuboid b) cubical

Step-by-step explanation:

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