B

1103164504

Level: 
B
An equilateral triangle is drawn on the wall. Inside the triangle, there is a circle with the radius of \( 1 \) metre inscribed. If a fly sits by chance in the triangle, what is the probability that it does not sit inside the circle? Round the result to \( 4 \) decimal places.
\( 0.3954 \)
\( 0.6046 \)
\( 0.3023 \)
\( 0.6977 \)

1103164503

Level: 
B
An equilateral triangle with a side of 3 metres is drawn on the wall. Inside the triangle, there is a circle with the diameter of 1 metre. If a fly sits by chance in the triangle, what is the probability that it does not sit inside the circle? Round the result to 4 decimal places.
\( 0.7985 \)
\( 0.2015 \)
\( 0.8061 \)
\( 0.1939 \)

1003164502

Level: 
B
Suppose the points \( A \) and \( B \) are randomly placed on a circle with a radius \( r \). What is the probability that the distance between \( A \) and \( B \) (length of the chord \( AB \)) is at least \( r \)?
\( \frac23 \)
\( \frac13 \)
\( \frac16 \)
\( \frac56 \)
\( \frac12 \)

1003164501

Level: 
B
In the house with a \( 7 \) metre high ground storey and \( 6 \) other storeys (\( 5 \) metres high each), there is a lift. On each storey, it is possible to enter this lift through a glass door that is \( 2 \) metres high. The lift malfunctioned and stopped somewhere on its way. What is the probability that (at the moment of stoppage) it would not be possible to see out of the lift only the wall of the lift shaft?
\( 0.7500 \)
\( 0.7838 \)
\( 0.7188 \)
\( 0.7647 \)
\( 0.7353 \)
\( 0.7568 \)

1003170503

Level: 
B
Find the volume (in liters) and the surface area (in \( \mathrm{dm}^2 \)) of a beach ball with diameter of \( 200\,\mathrm{mm} \). Round your result to \( 1 \) decimal place.
\( V=4.2\,\mathrm{l} \), \( S=12.6\,\mathrm{dm}^2 \)
\( V=42\,\mathrm{l} \), \( S=1.3\,\mathrm{dm}^2 \)
\( V=33.5\,\mathrm{l} \), \( S=12.6\,\mathrm{dm}^2 \)
\( V=4.2\,\mathrm{l} \), \( S=50.3\,\mathrm{dm}^2 \)

1003170501

Level: 
B
Find the volume and the surface area of a sphere with radius of \( 6\,\mathrm{cm} \). Leave your answer in terms of \( \pi \).
\( V=288\pi\,\mathrm{cm}^3 \), \( S=144\pi\,\mathrm{cm}^2 \)
\( V=144\pi\,\mathrm{cm}^3 \), \( S=288\pi\,\mathrm{cm}^2 \)
\( V=1728\pi\,\mathrm{cm}^3 \), \( S=144\pi\,\mathrm{cm}^2 \)
\( V=36\pi\,\mathrm{cm}^3 \), \( S=36\pi\,\mathrm{cm}^2 \)