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# Question 5

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?

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From the question statement, we have

Edge of a cube = 10 cm

Length, l = 12.5 cm

Height, h = 8 cm

(i) Find the lateral surface area for both the figures

\begin{aligned} &\text { Lateral surface area of cubical box }=4(\text { edge })^{2}\\ &=4(10)^{2}\\ &=400 \mathrm{cm}^{2} \end{aligned}

Lateral surface area of cubodal box =2[lh + bh]

= [2(12.5 × 8 + 10 × 8)]

= (2 × 180) = 360

\text { Therefore, Lateral surface area of cubodal box is } 360 \mathrm{cm}^{2} \ldots . .(2)

From (1) and (2), lateral surface area of the cubical box is more than the lateral surface area of the

cubodial box. The difference between both the lateral surfaces is, 40 \mathrm{cm}^{2}.

(Lateral surface area of cubical box - Lateral surface area of cuboidal \left.\mathrm{box}=400 \mathrm{cm}^{2}-360 \mathrm{cm}^{2}=40 \mathrm{cm}^{2}\right)

(ii) Find the total surface area for both the figures The total surface area of the cubical box = 6(\operatorname{edge})^{2}=6(10 \mathrm{cm})^{2}=600 \mathrm{cm}^{2} \ldots(3)

The total surface area of a cuboidal box

\begin{array}{l} =2[\mathrm{lh}+\mathrm{bh}+1 \mathrm{b}] \\ =[2(12.5 \times 8+10 \times 8+12.5 \times 100] \end{array}

= 610

This implies total surface area of the cuboidal box is 610 \mathrm{cm}^{2} . .(4)

From (3) and (4), the total surface area of the cubical box is smaller than that of the cuboidal box. And

their difference is 10 \mathrm{cm}^{2}.

Therefore the total surface of the cubical box is smaller than that of the cuboidal box by 10 \mathrm{cm}^{2}.

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