B

1003077113

Level: 
B
The curved surface of a cone has an area of \( 4.15\,\mathrm{cm}^2 \). If we flatten it into a plain, we get a sector of a circle with the central angle of \( 126^{\circ} \). Calculate the volume of this cone. Round the result to two decimal places.
\( 0.88\,\mathrm{cm}^3 \)
\( 0.62\,\mathrm{cm}^3 \)
\( 0.15\,\mathrm{cm}^3 \)
\( 311.00\,\mathrm{cm}^3 \)

1003077112

Level: 
B
The length of a circular arc with the central angle of \( 3.5 \) radians is \( 82\,\mathrm{cm} \). Calculate the radius of the corresponding circle. Round the result to two decimal places.
\( 23.43\,\mathrm{cm} \)
\( 287.00\,\mathrm{cm} \)
\( 1.59\,\mathrm{cm} \)
\( 4217.40\,\mathrm{cm} \)

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.
\( 19\,\mathrm{m} \)
\( 10\,\mathrm{m} \)
\( 15\,\mathrm{m} \)
\( 25\,\mathrm{m} \)

1103077210

Level: 
B
The picture shows a roundabout with the radius of \( 6\,\mathrm{m} \). Inside the roundabout there is a flower bed, which has the shape of an equilateral triangle inscribed in it. The remaining part inside the roundabout is the lawn. Calculate the area of the lawn.
\( 66.33\,\mathrm{cm}^2 \)
\( 46.77\,\mathrm{cm}^2 \)
\( 113.10\,\mathrm{cm}^2 \)
\( 24.66\,\mathrm{cm}^2 \)

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.
\( 2\,\mathrm{cm} \)
\( 4\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)