Question

The sum of length breadth and depth is19 cm and the length of its diagonal is 11 cm find the surface area of the cuboid

Answer 1

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Answer 2

Given:

• The sum of the length, breadth and depth of a cuboid is 19 cm.

• The length of diagonal = 11 cm.

To find out:

Find the Surface area of the cuboid

Solution:

Let the length, breadth and height of the cuboid be l cm, b cm, h cm respectively.

✪According to question:-

l + b + h = 19 .........( i )

Now,

Diagonal of cuboid = 11 cm

⇒ √ l² + b² + h² = 11

Squaring both sides

⇒ l² + b² + h² = 121 ........( ii)

Now,

l + b + h = 19

Squaring both sides

⇒ ( l + b + h )² = ( 19 )²

[ (a + b + c)³ = a² + b² + c² + 2(ab + bc + ca) ]

⇒ l² + b² + h² + 2( lb + bh + hl ) = 361

⇒ 121 + 2 ( lb + bh + hl ) = 361

⇒ 2 ( lb + bh + hl) = 240 cm²

⇒ Surface area of cuboid = 240 cm²