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प्रश्न
The sum of length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.
उत्तर
Let length, breadth and height of the cuboid be l cm, b cm and h cm, respectively.
Given: l + b + h = 38 cm and diagonal = 22 cm.
To find: total surface area of the cuboid
Diagonal of cuboid = `sqrt(l^2+b^2+h^2)`
`sqrt(l^2+b^2+h^2)=22`
`l^2+b^2+h^2=484" .........(i)"`
`"As "l+b+h=38`
`(l+b+h)^2=1444`
`l^2+b^2+h^2+2(lb+bh+lh)=1444`
`484=2(lb+bh+lh)=1444" .................From(i)"`
`2(lb+bh+lh)=960`
The surface area of the cuboid is 960 cm2.
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