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If the sum of three dimensions and the total surface area of a cuboidal box are 24 cm and 376 cm2 respectively, then the maximum length of a rod that can be put inside the box is?1). 7√3 cm2). 8√2 cm3). 5√2 cm4). 10√2 cm |
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Answer» As we know, total surface area of cuboid = 2(lb + BH + hl) And, maximum length of a ROD that can be put inside the BOX = √(L2 + b2 + h2) Given, l + b + h = 24 cm and 2(lb + bh + hl) = 376 cm2 As we know, (l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl) ⇒ 242 = l2 + b2 + h2 + 376 ⇒ l2 + b2 + h2 = 576 – 376 ⇒ l2 + b2 + h2 = 200 ⇒ √(l2 + b2 + h2) = √200 = 10√2 cm ∴ The maximum length of a rod that can be put inside the box is 10√2 cm |
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