Question

1) The dimensions of a closed cuboidal
packing case are in the ratio 5:4:3.
If the total surface area is 0.94 m², find
the dimensions of the cuboid,​

Answer 1

Given Question : -

• The dimensions of a closed cuboidal packing case are in the ratio 5:4:3. If the total surface area is 0.94 m², find the dimensions of the cuboid,

Answer :-

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{dimensions \: of \: cuboid \: are \: 5 :4 : 3} \\ &\sf{total \: surface \: area \: = 0.94 \: {m}^{2} = 9400 \: {cm}^{2} } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{dimensions \: of \: cuboid}  \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

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

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

$\begin{gathered}\begin{gathered}\bf Let - \begin{cases} &\sf{length \: = 5x} \\ &\sf{breadth \: = 4x}\\ &\sf{height \: = 3x} \end{cases}\end{gathered}\end{gathered}$

$\tt \:  \longrightarrow \: Total \: Surface \: area_{(Cuboid)}\: = 2(lb \: + bh \: + hl)$

$\tt \:  \longrightarrow \: 9400 = 2(5x \times 4x + 4x \times 3x + 3x \times 5x)$

$\tt \:  \longrightarrow \: 9400 = 2(20 {x}^{2} + {12x}^{2} + {15x}^{2} )$

$\tt \:  \longrightarrow \: 9400 = 2 \times 47 {x}^{2}$

$\tt \:  \longrightarrow \: 9400 = 94 {x}^{2}$

$\tt \:  \longrightarrow \: {x}^{2} = 100$

$\tt\implies \:x = 10$

$\begin{gathered}\begin{gathered}\bf Hence \: dimensions \: are- \begin{cases} &\sf{length \: = 5x = 50 \: cm} \\ &\sf{breadth \: = 4x = 40 \: cm}\\ &\sf{height \: = 3x = 30 \: cm} \end{cases}\end{gathered}\end{gathered}$

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More information:-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

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Answer 2

Answer:

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