Question

A cubical box has each edge 10 cm and another cuboidal box is 12.5cm 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?


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Answer 1

Step-by-step explanation:

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Answer 2

[Image refers in attachment.]

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From the question statement,

Edge of a cube = 10 cm

• Length, l = 12.5 cm
• Breadth, b = 10cm
• Height, h = 8 cm

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➊ Lateral surface area of cubical box

$\sf \longrightarrow 4 {a}^{2}$

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

$\sf \longrightarrow 4 \times 100$

$\sf \longrightarrow 400 \: {cm}^{2}$

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Lateral surface area of cuboidal box

$\sf \longrightarrow 2(l + b) \times h$

$\sf \longrightarrow 2(12.5 + 10) \times 8$

$\sf \longrightarrow 2 \times 22.5 \times 8$

$\sf \longrightarrow 360.0 \: {cm}^{2}$

$\sf \longrightarrow 360 \: {cm}^{2}$

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➋ Surface area of cubical box

$\sf \longrightarrow 6 {a}^{2}$

$\sf \longrightarrow 6 \times {(10)}^{2}$

$\sf \longrightarrow 6 \times 100$

$\sf \longrightarrow 600 \: {cm}^{2}$

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Surface area of cuboidal box

$\sf \longrightarrow 2(lb + bh + lh)$

$\sf \longrightarrow 2(12.5 \times 10 + 10 \times 8 + 12.5 \times 8)$

$\sf \longrightarrow 2(125.0 + 80 + 100.0)$

$\sf \longrightarrow 2 \times 305$

$\sf \longrightarrow 610 \: {cm}^{2}$

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Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm².