Answer: C
Let the length of the rectangular box be \(a\) cm, the width be \(b\) cm, and the height be \(c\) cm. ∴ \(a + b + c = 24\) — (i) And, \(\sqrt{a^2 + b^2 + c^2} = 15\) — (ii) Now, \((a + b + c)^2 = 24^2\) i.e., \(a^2 + b^2 + c^2 + 2(ab + bc + ca) = 576\) i.e., \(15^2 + 2(ab + bc + ca) = 576\) i.e., \(2(ab + bc + ca) = 576 - 225\) i.e., \(2(ab + bc + ca) = 351\) ∴ The total surface area of the rectangular box is 351 square cm.
Let the length of the rectangular box be \(a\) cm, the width be \(b\) cm, and the height be \(c\) cm. ∴ \(a + b + c = 24\) — (i) And, \(\sqrt{a^2 + b^2 + c^2} = 15\) — (ii) Now, \((a + b + c)^2 = 24^2\) i.e., \(a^2 + b^2 + c^2 + 2(ab + bc + ca) = 576\) i.e., \(15^2 + 2(ab + bc + ca) = 576\) i.e., \(2(ab + bc + ca) = 576 - 225\) i.e., \(2(ab + bc + ca) = 351\) ∴ The total surface area of the rectangular box is 351 square cm.