B

1103170702

Level: 
B
Let there be a cone with the base diameter of \( 8\,\mathrm{cm} \) and the slant height of \( 5\,\mathrm{cm} \). Find the volume and surface area of the cone. Leave your answer in terms of \( \pi \).
\( V=16\pi\,\mathrm{cm}^3 \), \( S=36\pi\,\mathrm{cm}^2 \)
\( V=64\pi\,\mathrm{cm}^3 \), \( S=104\pi\,\mathrm{cm}^2 \)
\( V=64\pi\,\mathrm{cm}^3 \), \( S=104\pi\,\mathrm{cm}^2 \)
\( V=16\pi\,\mathrm{cm}^3 \), \( S=28\pi\,\mathrm{cm}^2 \)

1103170701

Level: 
B
Let there be a cone with the base radius of \( 6\,\mathrm{cm} \) and the perpendicular height of \( 8\,\mathrm{cm} \). Find the volume and surface area of the cone. Leave your answer in terms of \( \pi \).
\( V=96\pi\,\mathrm{cm}^3 \), \( S=96\pi\,\mathrm{cm}^2 \)
\( V=96\pi\,\mathrm{cm}^3 \), \( S=84\pi\,\mathrm{cm}^2 \)
\( V=288\pi\,\mathrm{cm}^3 \), \( S=84\pi\,\mathrm{cm}^2 \)
\( V=16\pi\,\mathrm{cm}^3 \), \( S=96\pi\,\mathrm{cm}^2 \)

1103165906

Level: 
B
The volume of a cylinder with the height of \( 12\,\mathrm{cm} \) is \( 60\,\mathrm{cm}^3 \). Find the surface area of this cylinder. Round your result to \( 2 \) decimal places.
\( 105.12\,\mathrm{cm}^2 \)
\( 52.56\,\mathrm{cm}^2 \)
\( 135.54\,\mathrm{cm}^2 \)
\( 210.24\,\mathrm{cm}^2 \)

1103165905

Level: 
B
How much paper do we need to label the can of peas with diameter of \( 10\,\mathrm{cm} \) and height of \( 20\,\mathrm{cm} \)? (Label covers the side of the can completely, the bottom and the top base are not labelled.) Round your result to \( 1 \) decimal place.
\( 628.3\,\mathrm{cm}^2 \)
\( 1256.6\,\mathrm{cm}^2 \)
\( 314.2\,\mathrm{cm}^2 \)
\( 785.4\,\mathrm{cm}^2 \)

1003165904

Level: 
B
How many litres of water can a cylinder-shaped plastic barrel with diameter of \( 30.48\,\mathrm{cm} \) and height of \( 51\,\mathrm{cm} \) hold? Round your result to \( 1 \) decimal place.
\( 37.2\,\mathrm{l} \)
\( 148.9\,\mathrm{l} \)
\( 372.1\,\mathrm{l} \)
\( 62.3\,\mathrm{l} \)

1003165902

Level: 
B
Find the capacity of a garden pool in the shape of a cylinder with the diameter of \( 366\,\mathrm{cm} \) and the height of \( 0.91\,\mathrm{m} \). Round your result to \( 2 \) decimal places.
\( 9.57\,\mathrm{m}^3 \)
\( 38.30\,\mathrm{m}^3 \)
\( 957.74\,\mathrm{m}^3 \)
\( 19.15\,\mathrm{m}^3 \)

1103165901

Level: 
B
Find the volume and the surface area of a cylinder with the radius \( 3\,\mathrm{cm} \) and the height \( 8\,\mathrm{cm} \) (see the picture). Give your result in terms of \( \pi \).
\( V=72\pi\,\mathrm{cm}^3 \), \( S=66\pi\,\mathrm{cm}^2 \)
\( V=144\pi\,\mathrm{cm}^3 \), \( S=198\pi\,\mathrm{cm}^2 \)
\( V=144\pi\,\mathrm{cm}^3 \), \( S=66\pi\,\mathrm{cm}^2 \)
\( V=72\pi\,\mathrm{cm}^3 \), \( S=198\pi\,\mathrm{cm}^2 \)

1103164506

Level: 
B
At night, a parachutist landed on the spot \( M \), which is \( 3\,\mathrm{km} \) and \( 4\,\mathrm{km} \) away from the two straight and mutually perpendicular roads \( p \) and \( q \) respectively (see the picture). From the landing point, the parachutist walks straight in a random direction at the constant speed of \( 6\,\mathrm{km}/\mathrm{h} \). What is the probability that he reaches one of the roads in less than an hour? Round the result to \( 4 \) decimal places. \[ \] Hint: In the case of linear motion with constant speed, the speed is equal to the ratio of the displacement and the time of motion.
\( 0.5505 \)
\( 0.4495 \)
\( 0.6011 \)
\( 0.3989 \)
\( 0.3511 \)
\( 0.6489 \)

1103164505

Level: 
B
Suppose we have a rectangular fish tank which is \( 4\,\mathrm{dm} \) long, \( 2\,\mathrm{dm} \) wide, and it is filled with water up to the height of \( 3\,\mathrm{dm} \). In its four bottom corners, there are jets through which a fresh air is driven into the water in specific intervals. The fresh air is driven to the distance of up to \( 5\,\mathrm{cm} \) from the tank corners. If a fish swims inside the tank, what is the probability that the fish will not be hit by the stream of bubbles, at the moment when all four jets are acting? The fish dimensions can be neglected, round the result to \( 4 \) decimal places.
\( 0.9891 \)
\( 0.0109 \)
\( 0.9984 \)
\( 0.0016 \)
\( 0.9782 \)
\( 0.0218 \)