Q6 of 67 Page 187

The sum of length, breadth and height of a cuboid is 19 cm. If length of the diagonal is 11 cm then calculate the total surface area of the cuboid.

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


Given:


l + b + h = 19 cm


length of diagonal = 11 cm


length of diagonal of a cuboid =


⇒ = 11 cm


Squaring both sides we get


⇒ l2 + b2 + h2 = 121


Using identity (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac


⇒ (l + b + h)2 = l2 + b2 + h2 + 2lb + 2bh + 2hl


Substituting given values


⇒ 192 = 121 + 2 × (lb + bh + hl)


⇒ 361 = 121 + 2 × (lb + bh + hl)


⇒ 2 × (lb + bh + hl) = 361 – 121


⇒ 2 × (lb + bh + hl) = 240 cm2


Therefore, total surface area of cuboid is 240 cm2


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