Question

2 cubes each of volume 64 $c{m}^3$ are joined end to end. Find the surface area of the resulting cuboid.

Answer 1

Side of cube
$=\sqrt[3]{3Volume}$
$=\sqrt[3]{364}=4$
Length of new cuboid = 8 cm ( 4 + 4) , height = 4 cm, width = 4 cm
Surface area can be calculated as follows:
$=2(lb+lh+bh)$
$=2(8\times 4+8\times 4+4\times 4)$
$2\times 80=160c{m}^2$
Alternate Method:
Surface area of cube $=6\times sid{e}^2$
When two cubes are joined end to end, then out of 12 surfaces; two surfaces are lost due to joint. Thus, we need to take surface area of 10 surfaces and hence surface area can be given as follows:
$=10\times sid{e}^2=10\times 4^2=160c{m}^2$