Question

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 cm²

• 125 cm²

•  236 cm²

• 486 cm²

Answer 1

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 - ( l² + b² + h² ) 

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

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

=361-125

=236 cm²

Thus, the surface area is 236 cm²