B4. In the figure below, the floor plan of Petra's living room is drawn. Petra will build a glazed veranda over the entire circular arc at a height of $2 \mathrm{~m}$. What is the minimum number of square meters of glass she will need? Round the result to two decimal places.

![](https://cdn.mathpix.com/cropped/2024_06_07_c7870cece3ffb80afd9eg-5.jpg?height=576&width=828&top_left_y=1411&top_left_x=634)

## 8th Mathematics Knowledge Competition for Vocational School Students Regional Competition, April 2, 2008

## Solutions to the Problems and Scoring

## PROBLEMS SET A

In the table, the correct answers to the multiple-choice questions are recorded. We score each correct answer with 2 points, deduct 0.5 points for an incorrect answer, and 0 points if the question is not answered.

| A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| E | D | D | B | C | B | B | C | E | C |
B4 A covered veranda represents $\frac{3}{4}$ of the lateral surface of a cylinder that is $2 \mathrm{~m}$ high and has a base that is a circle with a radius of $150 \mathrm{~cm}$. The area of the covered veranda is: $S=\frac{3}{4} \cdot 2 \pi r \cdot v=\frac{3}{4} \cdot 2 \pi \cdot 150 \mathrm{~cm} \cdot 200 \mathrm{~cm}=141300 \mathrm{~cm}^{2}=14.13 \mathrm{~m}^{2}$.

Finding: The length of the arc is $\frac{3}{4}$ of the circumference of the circle. $1 \mathrm{t}$

![](https://cdn.mathpix.com/cropped/2024_06_07_c7870cece3ffb80afd9eg-8.jpg?height=60&width=1679&top_left_y=1786&top_left_x=228)

Calculated area: $S=141300 \mathrm{~cm}^{2}=14.13 \mathrm{~m}^{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .2$ t

Written answer, e.g.: For the glazing of the veranda, at least $14.13 \mathrm{~m}^{2}$ of glass will be needed. $1 \mathbf{t}$ Note: If the required unit is not included in the answer, the contestant receives 0 points.