Question

The sum of the length, breadth and height of a cuboid is 6√3cm and the length of its diagonal is 2√3cm. The total surface area of the cuboid is 

(a) 48 cm² 

(b) 72 cm² 

(c) 96 cm² 

(d) 108 cm²

Answer 1

(c) 96 cm² 

l + b + h = 6√3 ----(1)

\(\sqrt{l^2 +b^2 +h^2}=2\sqrt{3}\)

⇒ l² + b² + h² = 12 ---(2)

Now,

(l+b+h)² = l² + b² + h² + 2(lb+bh+hl)

⇒ 2(lb+bh+hl) = (l+b+h)² - (l²+b²+h²)

= (6√3)² - 12 (From (1) & (2))

= 108 - 12

= 96 cm²