Math, asked by kuchbhi6623, 1 year ago

The surface area of cuboud is 3328 m^2 if its xomensions are the ratio are inthe ratio 4:3:2 find volume

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Answered by sharmavijaylaxmi54
0

Answer:12,288 m^3

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Answered by TRISHNADEVI
4

 \huge{ \underline{ \overline{ \mid{ \mathfrak{ \pink{ \:   \: SOLUTION \:  \: } \mid}}}}}

 \underline{ \mathfrak{ \: Given, \: }} \\  \\  \mathtt{Surface  \:  \: area  \:  \: of \:  \:  the  \: cuboid = 3328 \: m {}^{3} } \\  \\  \text{Dimentions of the cuboid are in } \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \text{the ratio = 4 : 3 : 2} \\  \\  \\  \underline{ \mathfrak{ \:  \: Suppose, \:  \: }} \\  \\   : \rightsquigarrow \:  \text{The length of the cuboid = 4x}  \\  \\   : \rightsquigarrow \: \text{The breadth of the cuboid = 3x} \\  \\  : \rightsquigarrow \:  \text{The heigth of the cuboid = 2x} \\  \\  \\  \underline{ \mathfrak{ \:  \: To  \:  \: find :- \:  \: }} \\  \\ \:  \:  \:  \:  \:  \:  \:   \text{  Volume \:  of \:  the  \: cuboid = ?}

 \underline{ \mathfrak{ \:  \: We \:  \:  know \:  \:  that, \:  \: }} \\  \\  \boxed{ \bold{ \: </p><p></p><p>Surface \:  \:  area \:  \:  of  \:  \: the  \:  \: cuboid = 2 (lb + bh + hl)}}

 \bold{ \underline{ \:  \: A.T.Q., \:  \: }} \\  \\   \:  \:  \:  \:  \:  \:  \:  \mathtt{2(4x.3x+3x.2x+2x.4x) = 3328} \\  \\  \mathtt{\Longrightarrow \: 2(12x {}^{2}  + 6x {}^{2}  + 8x {}^{2} ) = 3328} \\  \\  \mathtt{\Longrightarrow \: 2 \times 26x {}^{2}  = 3328} \\  \\  \mathtt{\Longrightarrow \: 52x {}^{2}  = 3328} \\  \\  \mathtt{\Longrightarrow \: x {}^{2}  =  \frac{3328}{52} } \\  \\  \mathtt{\Longrightarrow \:   x {}^{2}  = 64} \\  \\  \mathtt{\Longrightarrow \: x =  \sqrt{64} } \\  \\  \:  \:  \:  \:  \mathtt{ \therefore \:  \:x =  \pm \: 8 } \\  \\  \mathtt{ \:  \:  \:  \:  \: As  \:  \: the \:  \:  value \:  \:  of  \:   \: \red{x}  \:  \: can't \:  \:  be  \:  \: negative,} \\  \mathtt{so, \:  \:  \underline{ \:  \red{ x = 8 }\: }}

 \mathtt{ \therefore \:  \:Length ,l= 4x =(4  \times 8  )\:m = 32 \: m} \\  \\  \mathtt{ \rightsquigarrow \:  Breadth,b = 3x = (3 \times 8) \: m = 24 \: m} \\ \\   \mathtt{ \rightsquigarrow \:  Height,h = 2x = (2  \times  8) \: m = 16 \: m}

 \mathfrak{ \: Now,} \\  \\  \underline{ \mathfrak{ \:  \: We  \:  \: know  \:  \: that, \:  \: }} \\  \\ \boxed{ \bold{Volume  \:  \: of  \:  \: a  \:  \: cuboid = l \times b \times h}}

 \underline{ \mathtt{  \: \: Putting \:  \: the  \:  \: value \:   \: of \:  \:  \red{ l },  \red{b} \: \:   and \:  \:   \red{h }\:  \: in  \:  \: the  \:  \:}} \\  \underline{ \mathtt{ \:  \:  formula, we  \:  \: get \:  \: }} \\  \\  \mathtt{Volume =(32 \times 24 \times 16) \:  \: m {}^{3}  } \\  \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \mathtt{ = 12288 \:  \: m {}^{3} }

 \underline{ \bold{ \:  \:Volume \:   \: of \:  \:  the \:   \: cuboid = 12288 \: m {}^{3}  \:  \: }}

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