The sum of the length, the breadth, and the height of a cuboid is 38 cm, and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.
960 cm2
The correct answer is Option 2 i.e. 960 cm2.
length(l) + breadth(b) + height(h) = 38....(1)
Diagonal = \(\sqrt{l^2+b^2+h^2}\)
⇒ 222 = l2 + b2 + h2
⇒ l2 + b2 + h2 = 484.....(2)
⇒ (l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl)
⇒ 382 = 484 + 2(lb + bh + hl)
⇒ 1444 = 484 + 2(lb + bh + hl)
⇒ 2(lb + bh + hl) = 960
Total surface area(TSA) = 2(lb + bh + hl) = 960 cm2
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