Mathematics
In the figure (i) below, a cuboid is shown. The surface area of three faces are marked as x, y and z. In figure (ii), two such cuboids are stacked. Find the surface area of the new cuboid in figure (ii) in terms of x, y and z.
Mensuration
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Answer
Given,
Let the dimensions of the cuboid be :
Length = l
Breadth = b
Height = h
From the figure (i) the three faces have areas:
x = length × height = lh
y = breadth × height = bh
z = length × breadth = lb
When two identical cuboids, are stacked the height is doubled (2h), length (l) and breadth (b) will remain same.
In (ii) figure,
Surface area of top face = length × breadth = lb = z
Surface area of right vertical face = length × height = 2lh = 2x
Surface area of left vertical face = breadth × height = 2bh = 2y
Total surface area = 2x + 2y + z.
Hence, surface area of new cuboid = 2x + 2y + z.
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