Question

Two cubes, each of volume 512 $c{m}^3$ are joined end to end, find the surface area of the resulting cuboid.

Answer 1

Volume of each cube = 512 $c{m}^3$
$\therefore$ Edge of cube (a) = $\sqrt[3]{3512}=\sqrt[3]{38\times 8\times 8\times cm}$
= $\sqrt[3]{38^3}$ = 8 cm
Now by joining the two equal cubes of side 8 cm, the length of so formed cuboid (l)
= $2\times 8=16cm$
Breadth (b) = 8 cm
and height (h) = 8 cm
$\therefore$ Surface area = $2(l\times b+b\times h+h\times l)$
= $2(16\times 8+8\times 8+8\times 16)c{m}^2$
= $2(128+64+128)c{m}^2$
= $2\times 320=640c{m}^2$