# Length - 9th grade (14y) - math problems

- Cutting cone

A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Circle and square

An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD. - Observation tower

From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower? - Wire fence

The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure? - Average height

There are twice as many girls in the class as there are boys. The average height of girls is 177 cm, boys 186 cm. What is the average height of students in this class? - Two trains

The train runs at speed v1 = 72 km/h. The passenger, sitting in the train, observed that a train long l = 75m in 3 s passed on the other track in the opposite direction. Calculate the speed of this train. - 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) - 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? - Squares ratio

The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte - What percentage

What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km - Self-oscillation period

The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s. - Steps

Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter. - Hiking trail

The newly built hiking trail leads 25% through the field, 3/8 of the trail leads through the forest and the remaining 9 km along the river. How long is the train? - Triangular pyramid

A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm - Two chords

In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords. - Rotaty motion

What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling? - Newtonmeters

The driver loosened the nut on the car wheel with a wrench that held 20 cm from the axis of the bolt. He acted on the key with a force of 320N. At what moment did he act on the bolt? - Cylinder

The 1.8m cylinder contains 2000 liters of water. What area (in dm^{2}) of this container is the water? - Cheetah vs antelope

When the cheetah began chasing the antelope, the distance between them was 120 meters. Although the antelope was running at 72km/h, the cheetah caught up with it in 12 seconds. What speed was the cheetah running? - Construct rhombus

Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm

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