The sum of length, breadth and height of a cuboid is 10 cm and the length of the diagonal is √32 cm. Find the area of the surfaces of the cuboid.
WBBSE
Class X
Mathematics
Rectangular Parallelopiped or Cuboid
2
2025
Let l, b, h be the length, breadth, and height of the cuboid.
l + b + h = 10
Length of diagonal (d) = \sqrt{l^2 + b^2 + h^2}
Substituting d = √32, we get:
\sqrt{l^2 + b^2 + h^2} = \sqrt{32}
or, l2 + b2 + h2 = 32
(l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl)
Substituting values:
102 = 32 + 2(lb + bh + hl)
100 = 32 + 2(lb + bh + hl)
2(lb + bh + hl) = 68 cm²
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