Question

The dimensions of a metal block are $2.25m$ by $1.5m$ by $27cm.$ It is melted and recast into cubes, each of the side $45cm.$ How many cubes are formed $?$

Answer 1

$\text{Dimension of metal block}:$
$2.25m$ by $1.5m$ by $27cm$
$=2.25m$ by $1.5m$ by $0.27m$ $(\because 1m=100cm)$

$\Rightarrow \text{Volume of metal block}=2.25m\times 1.5m\times 0.27m$

$\text{Side of each cube}=45cm=0.45m$ $(\because 1m=100cm)$

$\Rightarrow \text{Volume of each cube}={\text{(side)}}^3$

$=(0.45m{)}^3$

$=0.45\times 0.45\times 0.45m^3$

$\therefore \text{Number of cubes that can be formed}$

$=\frac{\text{Volume of the metal block}}{\text{Volume of each cube}}$

$=\frac{2.25\times 1.5\times 0.27}{0.45\times 0.45\times 0.45}$

$=10$

Hence, $10$ cubes are formed from the metal block.