1003077207
Level:
B
Given a circle of which the area and the circumference have the same numerical value, determine the diameter of the circle in \( \mathrm{cm} \).
\( 4 \)
\( 2 \)
\( \sqrt2 \)
\( \pi \)
B
1103077206
Level:
B
The circumference of a semicircle is \( 10\,\mathrm{cm} \). Find its radius.
\( \frac{10}{\pi+2}\,\mathrm{cm} \)
\( \frac{10}{\pi}\,\mathrm{cm} \)
\( \sqrt{\frac{10}{\pi}}\,\mathrm{cm} \)
\( \frac{10}{\pi+1}\,\mathrm{cm} \)
1103077205
Level:
B
A farmer has a fenced rhombus shaped garden with a side length of \( 4\,\mathrm{m} \). At one corner where the angle between the sides is \( 60^{\circ} \) the farmer tied a goat (see the picture). Of what length has to be the rope so that the goat grazes down exactly half the area of the garden? Round the result to one decimal place.
\( 3.6\,\mathrm{m} \)
\( 3.2\,\mathrm{m} \)
\( 4.1\,\mathrm{m} \)
\( 2.9\,\mathrm{m} \)
1103077204
Level:
B
Given a circle, the length of the chord \( AB \) is \( 16\,\mathrm{cm} \) and the height \( v \) of the corresponding circular segment is \( 5\,\mathrm{cm} \) (see the picture). Calculate the area of the segment. Round the result to two decimal places.
\( 57.29\,\mathrm{cm}^2 \)
\( 55.12\,\mathrm{cm}^2 \)
\( 47.12\,\mathrm{cm}^2 \)
\( 63.12\,\mathrm{cm}^2 \)
1103077203
Level:
B
The tip of a minute hand is at distance of \( 15\,\mathrm{mm} \) from the clock centre. Calculate the length of the path the tip travels in \( 42 \) minutes. Round the result to two decimal places.
\( 65.97\,\mathrm{mm} \)
\( 94.20\,\mathrm{mm} \)
\( 35.27\,\mathrm{mm} \)
\( 72.12\,\mathrm{mm} \)
1103077201
Level:
B
The flower bed has the shape of a circle sector of radius \( 3\,\mathrm{m} \) with central angle \( 75^{\circ} \). Calculate the area of this flower bed. Round the result to two decimal places.
\( 5.89\,\mathrm{m}^2 \)
\( 1.96\,\mathrm{m}^2 \)
\( 11.78\,\mathrm{m}^2 \)
\( 9.34\,\mathrm{m}^2 \)
1003021905
Level:
B
Calculate the height between two floors if you know that the number of stairs between the floors is \( 16 \), the slope of the staircase is \( 30^{\circ} \) and the depth of a stair is \( 25\,\mathrm{cm} \).
\( \frac{400}{\sqrt3}\,\mathrm{cm} \)
\( \frac{25}{\sqrt3}\,\mathrm{cm} \)
\( 200\,\mathrm{cm} \)
\( 400\,\mathrm{cm} \)
1003021902
Level:
B
What is the width of a computer screen if the ratio of its width and height is \( 16:9 \) and the computer has \( 23 \)-inch monitor? Round the result to two decimal places. (\( 1 \) inch=\( 2.54\,\mathrm{cm} \))
\( 50.92\,\mathrm{cm} \)
\( 20.05\,\mathrm{cm} \)
\( 11.28\,\mathrm{cm} \)
\( 28.65\,\mathrm{cm} \)
1103021901
Level:
B
What is the slope of a staircase if the height of a stair is \( 15\,\mathrm{cm} \) and the depth of a stair is \( 30\,\mathrm{cm} \)?
\( 26.57^{\circ} \)
\( 63.43^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)
1103256902
Level:
B
The cucumber field has the shape of an isosceles right triangle. The length of its legs is \( 12\,\mathrm{m} \). Rotary sprinklers placed in its vertices have a reach of \( 6\,\mathrm{m} \). Find the area of the field that is not sprinkled with water. Round the result to two decimal places.
\( 15.45\,\mathrm{m}^2 \)
\( 41.10\,\mathrm{m}^2 \)
\( 16.29\,\mathrm{m}^2 \)
\( 15.25\,\mathrm{m}^2 \)