Question

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

Answer 1

Given:

The dimensions of a metal block are $2.25m$ by $1.5m$ by $27cm$.

$\Rightarrow l=2.25m$

$b=1.5m$ and $h=27cm$

Lets convert in to the units $cm$.

Since, $1m=100cm$

$\Rightarrow$ $l=2.25m=2.25\times 100cm=225cm$

$b=1.5m=1.5\times 100cm=150cm$ and $h=27cm$

We know that, Volume of cuboid $=l\times b\times h$

Volume of the block $=225cm\times 150cm\times 27cm$

After melting, the side of each cube is $45cm$

$\Rightarrow$ Volume of each cube $=(45cm{)}^3$ [Since, Volume of cube $=a^3$, where, $a$ is side of the cube.]

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

$=\frac{225cm\times 150cm\times 27cm}{(45cm{)}^3}$

$=\frac{225cm\times 150cm\times 27cm}{45cm\times 45cm\times 45cm}$

$=\frac{5cm\times 30cm\times 3cm}{1cm\times 9cm\times 5cm}$

$=\frac{30}{3}$

$=10$
Therefore, the number of cubes $=10$.