1.

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

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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