Question

The dimensions of a Cuboids are in the ratio 5:3:2.it's volume is 21870 cm cube .Find it's total surface area

Answer 1

I hope it will help you

Answer 2

The total surface area is 5022 sq. cm.

Step-by-step explanation:

Let the length of cuboid be 5x

Let the width of cuboid be 3x

Let the height of cuboid be 2x.

Since we have given that

Volume of cuboid = 21870

So, it becomes,

$Volume=l\times b\times h\\\\21870=5x\times 3x\times 2x\\\\21870=30x^3\\\\\dfrac{21870}{30}=x^3\\\\729=x^3\\\\x=9\ cm$

So, length becomes $5x=5\times 9=45\ cm$

width becomes $3x=3\times 9=27\ cm$

height becomes $2x=2\times 9=18\ cm$

So, the total surface area would be

$2(lb+bh+lh)\\\\=2(45\times 27+27\times 18+45\times 18)\\\\=2\times 2511\\\\=5022\ cm^2$

Hence, the total surface area is 5022 sq. cm.

# learn more:

The dimension of a cuboid are in the ratio 5 is to 3 is to 2 its volume is 21870 cm cube find its total surface area​

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