# Examples for 9th grade - page 20

- Cathethus and the inscribed circle

In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle. - Triangle KLB

It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o - Height

Calculate height of the equilateral triangle if its perimeter is 54? - Water container

Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container? - Lines

In how many points will intersect 11 different lines, where no two are parallel? - Subsets

How many is subsets of set ?? - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Distance

Calculate distance between two points Z[7; -9] and U[-10; -8]. - Icerink

Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water. - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - Salary

Clerk got to pay 1200 Euros in banknotes of 50 and 200 Eur. Total got 9 banknotes. How many was which? - Tank

In the middle of a cylindrical tank with a bottom diameter 350 cm is standing rod which is 31 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank? - Pizza

A school survey found that 9 out of 16 students like pizza. If 5 students are chosen at random, what is the probability that all 5 students like pizza? - Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:5:3. Determine the size of the angles of the triangle ΔABC. - Trains for people

It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 50 km, with regular train leave at 6:05 and arrive at 7:20, but train is late and has departure at 9:52 and arrive at 11:05. - ISO trapezium

Calculate area of isosceles trapezoid with base 53 long, leg 43 long and with the angle between the base and leg 70 degrees. - Map - climb

On the map of High Tatras in scale 1:25000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 156 mm. Altitude of this stations are 944 m and 1755 m. What is average angle of climb of this cable car track? - Triangular prism

Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume. - Two workers

Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker? - Cuboid

Find the cuboid that has the same surface area as the volume.

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