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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
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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 - ( 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
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