Question

The length, breadth and height of a cuboid are in the ratio of 4:2:1 and it's total surface area is 1372 metre square. Find the dimensions of the cuboid.​

Answer 1

$\large\underline\blue{\bold{Given \:  Question :-  }}$

• The length, breadth and height of a cuboid are in the ratio of 4:2:1 and it's total surface area is 1372 metre square. Find the dimensions of the cuboid.

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$\huge{AηsωeR} ✍$

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$\large\underline\blue{\bold{Given :-  }}$

• The length, breadth and height of a cuboid are in the ratio of 4:2:1 and it's total surface area is 1372 metre square.

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$\large\underline\blue{\bold{To \: Find :-  }}$

• The dimensions of the cuboid.

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$\large\underline\blue{\bold{Formula \: Used :-  }}$

${{ \boxed{{\bold\green{Total \: Surface \: Area_{(Cuboid)}\: = 2(lb + bh + hl)}}}}}$

$\begin{gathered}\begin{gathered}\bf where= \begin{cases} &\sf{l = length \: of \: cuboid} \\ &\sf{b = breadth \: of \: cuboid} \\ &\sf{h \: = height \: of \: cuboid}\end{cases}\end{gathered}\end{gathered}$

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$\large\underline\purple{\bold{Solution :- }}$

The length, breadth and height of a cuboid are in the ratio of 4:2:1.

$\begin{gathered}\begin{gathered}\bf Let= \begin{cases} &\sf{length \: of \: cuboid \: be \: : l = 4x} \\ &\sf{breadth \: of \: cuboid \: be: b = 2x}\\ &\sf{height \: of \: cuboid: be \: h = x } \end{cases}\end{gathered}\end{gathered}$

$\sf \:  T \: S \: A_{(Cuboid)}\: = 2(lb + bh + hl)$

$\sf \:  T \: S \: A_{(Cuboid)}\: =2(4x \times 2x + 2x \times x + x \times 4x)$

$\sf \:  T \: S \: A_{(Cuboid)}\: =2( {8x}^{2} + {2x}^{2} + {4x}^{2} )$

$\sf \:  T \: S \: A_{(Cuboid)}\: =2 \times {14x}^{2}$

$\sf \:  T \: S \: A_{(Cuboid)}\: =28 {x}^{2}$

$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

$\sf \:  T \: S \: A_{(Cuboid)}\: = \: 1372$

$\sf\implies \: {28x}^{2} = 1372$

$\sf\implies \: {x}^{2} = {\cancel\dfrac{1372}{28}49}$

$\sf\implies \:x = 7$

$\begin{gathered}\begin{gathered}\bf Dimensions = \begin{cases} &\sf{length : l = 4x = 4 \times 7 = 28 \: m} \\ &\sf{breadth : b = 2x = 2 \times 7 = 14 \: m}\\ &\sf{height : h = x = 7 \: m} \end{cases}\end{gathered}\end{gathered}$

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