Question

When water freezes its volume increases by 4$\mathrm{\%}$. What volume of water is required to make $221c{m}^3$ of ice?

Answer 1

Hint: We are given the percentage increase in volume of ice. Now by simply assuming an unknown variable for volume of water, we can add the increase in the volume to it and equate it to the required volume. Solving the obtained equation for the unknown variable, we can get the required volume for water.
Detailed step by step solution:
We are given that the volume of water increases by 4$\mathrm{\%}$ when we freeze it and we need to find the volume of water required to make 221$c{m}^3$ of ice.
Now let us assume an unknown variable for the volume of water required to make ice which has a volume of $221c{m}^3$. Let the volume of water required by $xc{m}^3$. Since in ice form, the volume is 4$\mathrm{\%}$ more than the volume in liquid state, we can write the following expression for volume, taking into consideration the volume of ice that we need to obtain.
$x+4\mathrm{\%}\text{ of }x=221c{m}^3$
This expression is obtained based on the fact that there is an increase of 4$\mathrm{\%}$ in the volume of water as we lower its temperature to freeze it to obtain ice which has a volume of $221c{m}^3$.
Now we can solve this equation in the following way.
$\begin{array}{c}x+{\displaystyle \frac{4x}{100}}=221\\ {\displaystyle \frac{100x+4x}{100}}=221\\ {\displaystyle \frac{104x}{100}}=221\\ \Rightarrow x=221\times {\displaystyle \frac{100}{104}}\\ \therefore x=212.5c{m}^3\end{array}$

Hence, we need $212.5c{m}^3$ of water if we want to obtain $221c{m}^3$ of ice upon freezing. This is the required answer.

Note: When matter is cooled, it contracts while when it is heated, it expands. But here we are saying that the volume of water increases when temperature is lowered. The reason behind this anomaly is the lattice structure of ice. The lattice structure of ice is such that there are many empty spaces between the molecules which leads to an increase in volume on freezing water.