Math, asked by vkayal, 3 months ago

the ratio of the sides of two cubes are 2:3,then the ratio of their total surface areas are​

Answers

Answered by OtakuSama
39

Correct Question:-

If the ratio of the sides of two cubes are 2:3, then what will be the ratio of their total surface areas?

Required Answer:-

Given:-

 \\  \sf{ \rightarrow{Ratio  \: of  \: the \:  sides  \: of  \: two \:  cubes  = 2 \ratio3}} \\  \\

To Find:-

  \\ \sf{ \rightarrow{The \: ratio \: of \: their \: total\: serface \: area}} \\  \\

Solution:-

Let ,

  \\  \sf{ \ratio \rightarrow{Side \: of \: first \: cube \: be =  \bold{2x}}}

 \\  \sf{ \ratio \rightarrow{Side \: of \: second \: cube \: be =  \bold{3x}}} \\  \\

As we know that:-

 \\  \underline{ \boxed{ \rm{ \blue{ \bold{Total \: serface \: area \: of \: a \: cube} = 6 {a}^{2} }}}} \\  \\

Therefore,

Total surface area of first cube:-

 \\  \sf{ \bold{6 \times (2x) {}^{2} }}  = 6 \times 4 {x}^{2}  =  \orange{24 {x}^{2} } \\  \\

Total surface area of second cube:-

 \\   \sf{ \bold{6 \times (3x) {}^{2}} = 6 \times 9 {x}^{2}   = \orange{ 54 {x}^{2} }} \\  \\

Now,

  \\ \sf{Ratio \: of \: their \: surface \: area =  \bold{ \frac{24 {x}^{2} }{54 {x}^{2} } }}

 \\ \sf{ \implies{Ratio \: of \: their \: surface \: area =  \bold{ \large{ { \frac{4}{9}  } }}}}

 \\  \sf{ \therefore{Ratio \: of \: their \: surface \: area =   \red{4 \ratio9}}}

  \\  \\\underline{\boxed{ \green{ \therefore{\rm{Ratio \: of \: their \: surface \: area = \bold{ 4 \ratio9}}}}}}

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