Question

Three cubes of side $4cm$ each are joined end to end to form a cuboid.The surface area the resulting cuboid and total surface area of the three cubes are in the respective ratio of ______ ?

Answer 1

When such three cube are joined end to end then length(l) of resulting cuboid $=12cm$

or width (b) of resulting cuboid $=4cm$

and height (h) of resulting cuboid $=4cm$

surface area of resulting cuboid $=2(lb+bh+hl)$

$=2(12\times 4+4\times 4+4\times 12)$

$=2(48+16+48)$

$=2(96+16)$

$=2\left(112\right)=224c{m}^2$

Surface area of cube $=6l^2$

$=6\times (4{)}^2=256c{m}^2$

Ratio $=\frac{\text{area of cuboid}}{\text{area of cube}}=\frac{224}{256}=\frac{56}{64}=\frac{7}{8}$