The sum of the length, breadth and height of a cuboid is 24 cm, and the length of its diagonal is 15 cm. The area of its total surface is :

1. 348 cm²

2. 349 cm²

3. 350 cm²

4. 351 cm²

Given,

Sum of dimensions : l + b + h = 24

Length of diagonal (d) = 15 cm.

We know that,

Diagonal of cuboid (d) = $\sqrt{l^2 + b^2 + h^2}$

⇒ 15 = $\sqrt{l^2 + b^2 + h^2}$

Squaring on both sides,

⇒ 15² = $(\sqrt{l^2 + b^2 + h^2})^2$

⇒ 225 = l² + b² + h²

By formula,

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

By substituting the values we get,

⇒ (24)² = 225 + 2(lb + bh + hl)

⇒ 576 = 225 + 2(lb + bh + hl)

⇒ 2(lb + bh + hl) = 576 - 225

⇒ 2(lb + bh + hl) = 351

Since, Total surface area of cuboid = 2(lb + bh + hl)

∴ Total surface area of cuboid = 351 cm².

Hence, option 4 is the correct option.