Circles

1103077109

Level: 
B
Two quarter circles are inscribed in the square with sides of \( 2\,\mathrm{dm} \). The centres of the quarter circles are at the opposite vertices of the square (see the picture). Calculate the area of the region between the quarter circles. Round the result to two decimal places.
\( 2.28\,\mathrm{dm}^2 \)
\( 3.14\,\mathrm{dm}^2 \)
\( 21.12\,\mathrm{dm}^2 \)
\( 1.72\,\mathrm{dm}^2 \)

1103077111

Level: 
B
A piece of land in the shape of a circular sector with central angle of \( 60^{\circ} \) needs to be fenced. We have used \( 10 \) metres of wire mesh on the curved part of the fence. How many conventional metres of mesh still have to be purchased? Round the result to the nearest metre.
\( 19\,\mathrm{m} \)
\( 10\,\mathrm{m} \)
\( 15\,\mathrm{m} \)
\( 25\,\mathrm{m} \)

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.
\( 5.89\,\mathrm{m}^2 \)
\( 1.96\,\mathrm{m}^2 \)
\( 11.78\,\mathrm{m}^2 \)
\( 9.34\,\mathrm{m}^2 \)

1103077202

Level: 
B
Let \( ABCDEF \) be a regular hexagon. Six circles of equal radii are drawn touching each other with their centres at the hexagon vertices (see the picture). Calculate the area of the coloured region inside the hexagon if you know that the perimeter of the hexagon \( ABCDEF \) is \( 36\,\mathrm{cm} \). Round the result to two decimal places.
\( 36.98\,\mathrm{cm}^2 \)
\( 93.53\,\mathrm{cm}^2 \)
\( 65.26\,\mathrm{cm}^2 \)
\( 25.37\,\mathrm{cm}^2 \)

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.
\( 65.97\,\mathrm{mm} \)
\( 94.20\,\mathrm{mm} \)
\( 35.27\,\mathrm{mm} \)
\( 72.12\,\mathrm{mm} \)

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.
\( 57.29\,\mathrm{cm}^2 \)
\( 55.12\,\mathrm{cm}^2 \)
\( 47.12\,\mathrm{cm}^2 \)
\( 63.12\,\mathrm{cm}^2 \)

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.
\( 3.6\,\mathrm{m} \)
\( 3.2\,\mathrm{m} \)
\( 4.1\,\mathrm{m} \)
\( 2.9\,\mathrm{m} \)

1103077209

Level: 
B
A semicircle is inscribed in a triangle \( KLM \) so that the diameter of the semicircle is parallel to side \( KL \) (see the picture). The length of \( KL \) is \( 8\,\mathrm{cm} \) and the height to side \( KL \) is \( 4\,\mathrm{cm} \) long. Determine the radius of the semicircle.
\( 2\,\mathrm{cm} \)
\( 4\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)