Question:
Two cubes, each of volume 64 cm3, are joined end to end. Find the total surface area of the resulting cuboid.
Solution:
Volume of the cube = a3
Therefore,
$a^{3}=64$
$\Rightarrow a^{3}=(4)^{3}$
$\Rightarrow a=4 \mathrm{~cm}$
Each side of the cube = 4 cm
Then,
Length of the cuboid $\Rightarrow(2 \times 4) \mathrm{cm}=8 \mathrm{~cm}$
Breadth of the cuboid = 4 cm
Height of the cuboid = 4 cm
Total surface area of the cuboid $=2(l b+b h+l h)$
$=2[(8 \times 4)+(4 \times 4)+(8 \times 4)] \mathrm{cm}^{2}$
$=(2 \times 80) \mathrm{cm}^{2}$
$=160 \mathrm{~cm}^{2}$
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