Circles

2000005902

Level: 
A
What is the measure of the angle made by two line-segments marked in the clock face (see the picture)? One segment is connecting points \(1\) and \(3\), second segment is connecting points \(5\) and \(3\).
\( 120^{\circ}\)
\( 135^{\circ}\)
\( 60^{\circ}\)
\( 240^{\circ}\)

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