# Examples for 9th grade

- Cone roof

How many m^{2}of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays. - Double probability

The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice? - Bricklayers

The first bricklayer would build a wall in 3 days, the second in 4 days. The first bricklayer worked alone for a day, then the second bricklayer came to his aid and they finished the work together. How long did it take to build the wall? - Spherical cap

The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - The rescue helicopter

The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site? - Wall and body diagonals

The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals. - Embankment

The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m^{3}of soil is in the embankment? - Similarity of two triangles

The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity) - Clock hands

Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours. - A kite

Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain? - Water mixing

There are 5 liters of water at 75°C in the pot, how much water at 10°C do we have to add to the resulting temperature of 55°C? - Working together

Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone? - The copper wire

The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg? - Black diamond run

Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet. - The shooter

The shooter heard the impact of the bullet on the target in one second after the shot. The bullet was moving at an average speed of 500 m/s. Calculate with speed of sound of 340 m/s. Determine the distance of the target. - Christmas holidays

How many percent take Christmas holidays lasting 18 days from a school year that lasts 303 days? Round the result to two decimal places - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Sweets, candy

Grandfather gave out sweets to four children. At the last moment, two more children came, so in order to have them all the same, each of the four children would receive four candies less than they would have received if they had not. How much did my grand - Hectares of forest

12 workers plant 24 ha of forest in 6 days. In how many days will 15 people and 12 people plant the same area? - Height of the cuboid

Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?

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