The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is \(5\sqrt{5}\) cm, then its surface area is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 236 cm2
For a cuboid with sides \(l\), \(b\), \(h\), the diagonal is \(\sqrt{l^2+b^2+h^2}\) and the surface area is \(2(lb+bh+hl)\). Squaring the sum of the sides joins the two: \((l+b+h)^2=(l^2+b^2+h^2)+2(lb+bh+hl)\), so the surface area is the square of the sum minus the square of the diagonal.
\((l+b+h)^2=19^2=361\)
\(l^2+b^2+h^2=(5\sqrt{5})^2=125\)
Surface area \(=361-125=236\,\mathrm{cm^2}\)