Question

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

greater lsa is the cuboidal box

cubical box has smaller tsa

Answer 2

Given -

A cubical box having the edges (sides) 10 cm.

A cuboidal box having the

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀length as 12.5 cm

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀Breadth as 10 cm

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀Height as 8 cm.

To find -

• Which box has the greater lateral surface area and by how much?
• Which box has the smaller total surface area and by how much?

Solution -

Let's take the cube first

1. sides = 10 cm

Lateral surface of a cube or cubical box = ${4a}^{2}$

$4 \times {(10)}^{2}$

$4 \times 100 \: cm^{2}$

$400 \: cm$

2. Total surface are of the cube or cubical box = ${6a}^{2}$

$6 {(10)}^{2} \: cm$

$6 \times 100 \: cm$

$600 \: cm ^{2}$

ii) Now let's take the cuboidal box -

Length = 12.5 cm

Breadth = 10 cm

Height = 8 cm

1. Lateral surface of cuboid or cuboidal box = 2h (l+b)

$2 \times 8(12.5 + 10)$

$16 \times 22.5$

$360.0 = > 360 \: cm^{2}$

2. Total surface area of a cuboid or cuboidal box = 2(lb + bh + hl)

$2(12.5 \times 10 + 10 \times 80 + 8 \times 12.5)$

$2(125 + 80 + 100)$

$2 \times 305$

$610 {cm}^{2}$

Conclusion -

• Cubical box's lateral surface area is greater than cuboidal box lateral surface area by 40 cm.
• In the second case cubical box's total surface area is smaller than cuboidal box by 10cm.