Rosa won a perfume bottle in the shape of a cylinder with a base radius of $7 \mathrm{~cm}$ and a height of $10 \mathrm{~cm}$. After two weeks of using the perfume, $0.45 \mathrm{~l}$ remained in the bottle. What fraction represents the volume that Rosa has already used?
The volume of a cylinder is the product of the base area and the height. Since the radius of the base is $7 \mathrm{~cm}$, the base area is: $\pi \times 7^{2}$, and thus the volume of the glass is

$$
\pi \times 7^{2} \times 10 \mathrm{~cm}^{3}=490 \pi \mathrm{~cm}^{3}=\frac{490 \pi}{1000} \mathrm{~dm}^{3}=0.49 \pi \text { liters }
$$

remembering that $1000 \mathrm{~cm}^{3}=1 \mathrm{~dm}^{3}=1$ liter.

After two weeks, 0.45 liters of perfume remained, so she used $(0.49 \pi-0.45)$ liters. Therefore, the fraction representing the volume used is:

$$
\frac{\text { volume used }}{\text { total volume }}=\frac{0.49 \pi-0.45}{0.49 \pi}=\frac{49 \pi-45}{49 \pi}
$$