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  • The length,breadth and height of a cuboid are in the ratio 7:6:5.If the surface area of the cuboid is 1926 cm^2,find 1-Volume 2-length of a diagonal of the cuboid.

The length,breadth and height of a cuboid are in the ratio 7:6:5.If the surface area of the cuboid is 1926 cm^2,find 1-Volume 2-length of a diagonal of the cuboid.

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Since the length,breadth and height of a cuboid are in the ratio 7:6:5,let its length=7x cm,breadth=6x cm and height=5x cm
Surface Area=2(7x imes6x+7x imes5x+6x imes5x)cm^2
Rightarrow 2(2 imes107)x^2cm^2=214x^2cm^2
According to the given question,214x^2=1926
Rightarrow x^2=9Rightarrow x=3
Therfore the length=(7 x 3)cm=21 cm,breadth=18 cm and height=15 cm

  1. The volume of the cuboid= (21 imes18 imes15)cm^3=5670cm^3
  2. The length of the diagonal=sqrt21^2+18^2+15^2, cm=sqrt441+324+225, cm=sqrt990, cm=3sqrt110, cm
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Deependra Verma

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