1.1. The diagram below shows a drinking glass with an inner diameter of 50mm and a height h. Ignore the thickness of the glass. The volume of the glass is 250 cm³. Calculate the height h. 1.2 Water is now poured into the glass until it is 65% full. Calculate the total surface area coved by the water

The diameter is $50 \text{ mm}$.
The radius $r = \frac{50 \text{ mm}}{2} = 25 \text{ mm}$.
Since $1 \text{ cm} = 10 \text{ mm}$, the radius in centimeters is $r = \frac{25}{10} \text{ cm} = 2.5 \text{ cm}$.
The volume of the glass is given as $V = 250 \text{ cm}^3$.

The volume of a cylinder is given by $V = \pi r^2 h$.

The height $h$ is approximately $\boxed{12.73 \text{ cm}}$.

The glass is $65\%$ full, so the height of the water ($h_{water}$) is $65\%$ of the total height $h$.

The total surface area covered by the water includes:

• The area of the bottom circular base of the glass: $A_{bottom} = \pi r^2$
• The curved surface area of the glass in contact with the water: $A_{curved} = 2 \pi r h_{water}$
• The area of the top surface of the water: $A_{top} = \pi r^2$ The total surface area ($A_{total}$) is the sum of these three areas:

We have $r = 2.5 \text{ cm}$ and $h_{water} = \frac{26}{\pi} \text{ cm}$.

The total surface area covered by the water is approximately $\boxed{169.27 \text{ cm}^2}$.