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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. - Geometry

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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.

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Solution

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.

Concept: Surface Area of a Combination of Solids
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