Question

The length,breadth,height is in 3:2:5cm. find the total surface area of cuboid.​

Answer 1

Correct Question :

$\normalsize\sf\ If \: the \: Length,Breadth \: and \: height \: of \: cuboid \\ \normalsize\sf\ \: is \: in \: ratio \: of \: 3:2:5 \: cm. \: Find \: the \\ \normalsize\sf\ Total \: surface \: area \: of \: cuboid.$

$\rule{200}2$

AnswEr :

$\normalsize\bullet\:\sf\ Let \: the \: Length \: of \: Cuboid \: be \: \bf\ 3x \: cm$

$\normalsize\bullet\:\sf\ Let \: the \: Breadth \: of \: Cuboid \: be \: \bf\ 2x \: cm$

$\normalsize\bullet\:\sf\ Let \: the \: Height \: of \: Cuboid \: be \: \bf\ 5x \: cm$

⋆ Reference of Image is shown in diagram

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\put(8,5.5){3x \: cm}\put(4,6.3){2x \: cm}\put(11.2,7.5){5x \: cm}\end{picture}$

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☯ $\underline{\textsf{Let's \: head \: to \: the \: Question \: now:}}$

$\normalsize\sf{\boxed{\sf{Total \: surface \: area = 2(LB + BH + Hl) }}}$

$\normalsize\ : \implies\sf\ T.S.A = 2[ 3x \times\ 2x + 2x \times\ 5x + 5x \times\ 3x]$

$\normalsize\ : \implies\sf\ T.S.A = 2[ 6x^2 + 10x^2 + 15x^2]$

$\normalsize\ : \implies\sf\ T.S.A = 2[31x^2]$

$\normalsize\ : \implies\sf\ T.S.A = 2 \times\ 31x^2$

$\normalsize\ : \implies\sf\ T.S.A = 62x^2$

$\normalsize\ : \implies{\underline{\boxed{\sf \red{ T.S.A = 62x^2 \: cm^{2} }}}}$

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☯ $\underline{\textsf{Some \: important \: realted to \: to \: it:}}$

$\boxed{\begin{minipage}{6cm}\bf\underline{ Important formulae of Cuboid}\\ \\ \textsf{ \bullet\ Curved \: surface \: area = 2H(L + B) }\\ \\ \textsf{ \bullet\ Surface \: area = 2(LB + BH + HL) } \\ \\ \textsf{ \bullet\ Volume = L \times\ B \times\ H } \\ \\ \textsf{ \bullet\ Diagnol = \sqrt{L + B + H} }\end{minipage}}$

Answer 2

Answer:

According to the given question

total surface area of the cube is (62x^2) cm^2