Ex.11.3 Q1 Mensuration Solution - NCERT Maths Class 8

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Question

There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

 Video Solution
Mensuration
Ex 11.3 | Question 1

Text Solution

What is Known?

Dimensions of the cuboidal boxes.

What is unknown?

Surface area of the given figure

Reasoning:

The amount of material requires to make boxes will be equal to their respective surface area.

Steps:

Total surface area of the cuboid lateral surface \(=\) area of curved surface \(+ 2\; \times \) area of base

Total surface area of the cub \( = 6{(l)^2}\)

Total surface area of cuboid in figure

\[\begin{align} &= \! (hl \! + \! hb \! + \! hl \! + \! hb) \! + \! 2(lb)\\&= \! 2(hl \! + \! lb \! + \! hb)\\&= \! 2(60 \! \times \! 50 \! \times \! + \! 40 \! \times \! 50 \! + \! 60 \! \times \! 40)\,\rm{cm^2}\\&= \! 2(3000 \! + \! 2000 \! + \! 2400)\,\rm{cm^2}\\&= \! 14800\,\rm{m^2} \end{align}\]

Total surface area of cube in figure (b)

\[\begin{align} &= 6 \times {(l)^2}\\& = 6 \times {(50)^2}\\& = 6 \times 2500\\&= 15000\,\rm{cm^2}\end{align}\]

Thus, the cuboid box (a) requires lesser amount of material.

  
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