# Examples for 9th grade - page 48

- Aircrafts

Above the town hall tower flew the plane with constant speed 508 km/h and 15 minutes later the second plane at speed of 651 km/h. How long and how far from the town hall will be aircrafts caught up? - Inscribed rectangle

The circle area is 184. Determine the area of inscribed rectangle with one side 10 long. - 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. - Circle section

Equilateral triangle with side 50 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector. - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle. - 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. - n-gon II

What is the side length of the regular 9-gon circumscribed circle of radius 13 cm? - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Aircraft

The plane flies at altitude 6800 m. At the time of first measurement was to see the elevation angle of 20° and second measurement of the elevation angle of 34°. Calculate the distance the plane flew between the two measurements. - Sines

In ▵ ABC, if sin(α)=0.5 and sin(β)=0.1 calculate sin(γ) - Steamship

Between the two ports on the river is going steamship. The journey there and back takes 14:49. Downstream steamship traveling at 21 km/h, upstream 9 km/h. What is the distance between the ports? - Triangle ABC

Calculate the sides of triangle ABC with area 1789 cm^{2}and if a: b: c = 6:16:11 - Similarity

The area of the regular 5-gon is 505 cm^{2.}The area of similar 5-gon is 606 dm^{2.}What is the coefficient of similarity. - Car factory

Carmaker now produce 4 cars a day more than last year, so the production of 413448 cars will save just one full working day. How many working days needed to manufacture 413448 cars last year? - 2x cone

Circular cone height 60 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone. - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Cubes

Surfaces of cubes, one of which has an edge of 18 cm shorter than the other, differ by 7776 mm^{2.}Determine the length of the edges of this cubes. - Cone

Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume. - Glass of juice

Glass of juice shaped cylinder 16 cm height and base diameter of 10 cm is filled with juice so that the level is 3 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow. - Magnification of the square

If we increase the square side, increase the content of the 42 %. About what percentage was increased his sides?

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