Ex.11.3 Q4 Mensuration Solution - NCERT Maths Class 8

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Question

Rukhsar painted the outside of the cabinet of measure \(1\,\rm{m} \times 2\, \rm{m} \times \,1.5\, \rm{m.}\) How much surface area did she cover if she painted all except the bottom of the cabinet?

 Video Solution
Mensuration
Ex 11.3 | Question 4

Text Solution

What is Known?

Dimensions of the cuboid.

What is unknown?

 Surface area of cuboid that was palindrome.

Reasoning:

Surface area of bottom of the cuboid will be subtracted from the total surface area of the cabinet.

Steps:

Length (\(l\)) of the cabinet \(=\,2\,\rm{m}\)

Breadth (\(b\)) of the cabinet \(=1\,\rm{m}\)

Height (\(n\)) of the cabinet \(= 1.5\,\rm{m}\)

Area of the bottom of cabinet \( = (l \times b)\)

Total Surface area of the cabinet \( = 2(l \times b + b \times h + n \times l)\)

Area of the cabinet that was painted \(=\) (Total surface area of  the cabinet) \(-\) (Area of bottom of the cabinet)

\[\begin{align} &= 2(l \times b + b \times h + h \times l) - l \times b\\&= 2(b \times h + h \times l) + l \times b\\ &= [2 \times (1 \times 1.5 + 1.5 \times 2) + 2 \times 1]\,{{\rm{m}}^2}\\&= [2 \times 4.5 + 2]\,{{\rm{m}}^2}\\&= 11\,{{\rm{m}}^2} \end{align}\]

Hence, the required area \(= 11 \,\rm{m}^2\)

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