Examples for 9th grade - page 48
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.
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?
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'
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.
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.1 calculate sin(γ)
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 cm2 and if a: b: c = 6:16:11
The area of the regular 5-gon is 505 cm2. The area of similar 5-gon is 606 dm2. 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.
Surfaces of cubes, one of which has an edge of 18 cm shorter than the other, differ by 7776 mm2. Determine the length of the edges of this cubes.
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?