Question

Given that $\mathbf{1}\mathbf{}\mathit{c}\mathit{u}\mathit{b}\mathit{i}\mathit{c}\mathbf{}\mathit{c}\mathit{m}$ of marble weighs $\mathbf{0}\mathbf{.}\mathbf{25}\mathbf{}\mathit{k}\mathit{g}$, the weight of marble block $\mathbf{28}\mathbf{}\mathit{c}\mathit{m}$ in width and $\mathbf{5}\mathbf{}\mathit{c}\mathit{m}$ thick is $\mathbf{112}\mathbf{}\mathit{k}\mathit{g}$. Find the length of the block.

Answer 1

Step 1: Find the volume of the marble block

Let $l$ be the length of the marble block

Given,

Weight of $1c{m}^3$ of marble $=0.25kg$.

Wight of marble block which is $28cm$ in width and $5cm$ thick $=112kg$.

Volume of the marble block $=l\times 28\times 5$

$\therefore$ Volume of the marble block $=140l$

Step 2: Find the length $\mathit{l}$ of the marble block

Weight of marble block $=$ Volume of the marble block $\times$ Weight of $1c{m}^3$ of marble

$\Rightarrow 112=140l\times 0.25$

$\Rightarrow 112=35l$

$\Rightarrow l=\frac{112}{35}$

$\therefore l=3.2cm$

Hence, the length of the marble block is $3.2cm$.