Question

The sum of length, breadth and height of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.

Answer 1

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

l + b + h = 19 …(i)

and diagonal = 11

⇒ \(\sqrt { { l }^{ 2 }+{ b }^{ 2 }+{ h }^{ 2 } }\) = (11)²

⇒ l² + b² + h² = 121 …(ii)

Using (i), l + b + h = 19

Squaring both sides, we have

(l + b + h)² = 192

l² + b² + h² + 2 (lb + bh + hl) = 361

121 + 2 (lb + bh + hl) = 361

2 (lb + bh + hl) = 361 – 121

⇒ 2 (lb + bh + hl) = 240

Hence, the surface area of the cuboid is 240 cm².