Question

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid is $648$ $c{m}^2;$ find the length of edge of each cube. Also, find the ratio between the surface area of resulting cuboid and the surface area of a cube.

• A. $9$ cm and $3:1$
• B. $2$ cm and $3:1$
• C. $6$ cm and $3:1$
• D. $3$ cm and $3:1$

Answer 1

Answer: (C)

$6$ cm and $3:1$

Given, four identical cubes are joined end to end to form a cuboid. Let the side of cube be $a$, then length of cuboid thus formed be 4$a$ ,breadth be $a$, height be $a$. Surface area of resulting cuboid be 648${cm}^2$.
Total surface area of resulting cuboid$=2(lb+bh+lh)$
$or,648=2(4a\times a+a\times a+4a\times a)or,648=2\left(9a^2\right)or,648=18a^{2}or,a^2=36or,a=6cm$
Length of edge of cube$=6cm$
Surface area of cube$=6a^2=6\times 6^2=216{cm}^2$
Ratio of surface area of resulting cuboid to cube$=\frac{648{cm}^2}{216{cm}^2}=3:1$