Question

A cube of edge $3$ cm of iron weighs $12$ g. What is the weight of a similar cube of iron whose edge is $12$ cm?

• A. $768$ g
• B. $678$ g
• C. $964$ g
• D. $864$ g

Answer 1

The correct option is A $768$ g

We know, volume of cube $=(side{)}^3$.

In this case, side $=3$ cm.

Let us assume side as $a$.
$\therefore$ Volume of cube $=a^3$.

If side increases by $4$ (in our case new side is $12$ which is $4$ times $3$),

then volume of cube with new side as $12$ cm $=64a^3$
i.e., Volume increase by $64$ times.

$\therefore$ Volume of side $12$ cm $=$ $64$ $\times$ Volume of side $3$ cm
i.e., Mass of side $12$ cm $=$ $64$ $\times$ Mass of side $3$ cm .....(Because cubes are similar).
$\therefore$ The weight of a similar cube of iron, whose edge is $12$ cm $=64\times 3^3=768$ g.

Hence, option $A$ is correct.