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Question

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 02 Mark 2025

Answer

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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