Question

The diagonal of a gift box which is cuboidal in shape is of length$10\sqrt{5}$ cm and the sum of its length, breadth and depth is 38 cm.
What is the minimum area of gift paper required to wrap the box?

• A. 500 cm²
• B. 944 cm²
• C. 1444 cm²
• D. 1944 cm²
• E. 472 cm²

Answer 1

The correct option is B

944 cm²

(l +b+h) = 38 and so (l${}^2$ +b${}^2$ + h${}^2$) = (10$\surd$5)${}^2$ = 500

Now, (l + b + h)${}^2$ = 38${}^2$ = (l${}^2$+b${}^2$+h${}^2$) +2 (lb + bh + lh) = 1444

$\Rightarrow$ 2(lb + bh + lh) = (1444 – 500) = 944 $\therefore$Surface area = 944 cm${}^2$