Length and breadth of a cuboid is in the ratio of 4:5 and its height is 18 cm. Its Total surface area is 3384 cm2. Find its Length and breadth.
Answers
RequiredSolution:
\begin{gathered}\bf Given \begin{cases} & \sf{Total\:surface\:area= \bf{340cm^{2}}} \\ & \sf{Breadth\:or\:width= \bf{8cm}} \\ & \sf{Height= \bf{5cm}} \end{cases}\\ \\\end{gathered}
Given
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Totalsurfacearea=340cm
2
Breadthorwidth=8cm
Height=5cm
◾️We need to find its length.
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Acknowledgement —
\large{\star}{\boxed{\sf{\orange{T.S.A\:of\:cuboid=2(lb+lh+bh)}}}}{\star}⋆
T.S.Aofcuboid=2(lb+lh+bh)
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Let the length be l.
According to the question,
\implies{\sf{340cm^{2}=2\big[(l\times8)+(8\times5)+(5\times l)\big]}}⟹340cm
2
=2[(l×8)+(8×5)+(5×l)]
\implies{\sf{340cm^{2}=2\big[(8l)+(40)+(5l)\big]}}⟹340cm
2
=2[(8l)+(40)+(5l)]
\implies{\sf{340cm^{2}=2(13l+40)}}⟹340cm
2
=2(13l+40)
\implies{\sf{340=26l+80}}⟹340=26l+80
\implies{\sf{340-80=26l}}⟹340−80=26l
\implies{\sf{260=26l}}⟹260=26l
\implies{\sf{l=\dfrac{260}{26}}}⟹l=
26
260
\implies{\sf{l=10}}⟹l=10
Hence, the length is 10 cm.
And we are done! :D
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\Large{\underline{\underline{\sf{Extra\:shots:}}}}
Extrashots:
Cuboid
l = length
b = Breαdth
h = height
Totαl surfαce αreα of cuboid (T.S.A) = 2(lb+lh+bh)
Lαterαl surfαce αreα of cuboid (L.S.A) = 2(l+b)*h or 2(lh+bh)
Volume of cuboid = l*b*h
Cube
side = α
Totαl surfαce αreα of cube (T.S.A) = 6α²
Lαterαl surfαce αreα of cube (L.S.A) = 4α²
Volume of cube = α³