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MCQ

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is ` 5 sqrt(5)` cm. Its surface area is

#### Options

361 cm

^{2}125 cm

^{2}236 cm

^{2}486 cm

^{2}

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#### Solution

Let,

l → Length of the cuboid

b → Breadth of the cuboid

h → Height of the cuboid

We have,

l + b + h = 19 cm , diagonal of the cuboid

`( sqrt(l^2 + b^2 +h^2)) = 5 sqrt(5) cm `

We are asked to find the surface area

So, the surface area,

= 2 (lb + bh + hl )

= (l + b +h )^{2 }- ( l^{2 }+ b^{2} + h^{2} )

`=(l + b+ h) - ( sqrt (l^2 + b^2 + h^2 ))^2`

`=19^2 - (5sqrt(5))^2`

=361-125

=236 cm^{2}

Thus, the surface area is 236 cm^{2}

Concept: Surface Area of a Cuboid

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