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Surface area of a cuboidal box is 48 cm2 and the sum of all edges is 48 cm. What is the length of the diagonal?1). √50 cm2). √12 cm3). √48 cm4). √90 cm |
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Answer» Surface AREA of cuboid = 48 cm2 ⇒ 2(lb + bh + hl) = 48 ----- (1) ⇒ Sum of 12 EDGES = 48 ⇒ 4(l + b+ h) = 48 cm ⇒ l + b + h = 12 cm ----- (2) Diagonal of cuboid = $(\sqrt {{l^2} + {b^2} + {h^2}})$ ----- (3) Squaring (2) : (l + b + h)2 = 122 L2 + b2 + h2 + 2(lb + bh + hl) = 144 ⇒ Substituting from (1) and (3) Diagonal2 + 48 = 144 Diagonal2 = 144 – 48 = 96 ∴ Diagonal = √96 cm |
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