# Examples for 9th grade - page 13

1. Climb Road has climbing 1:27. How big is a angle corresponds to this climbing?
2. Tetrahedral pyramid Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
3. Square 2 Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
4. Motion From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus?
5. Dice How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
6. Rotary cone Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
7. Sale If the product twice price cut by 25%, what percentage was price cut in total?
8. Square grid Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
9. Football league In the 5th football league is 10 teams. How many ways can be filled first, second and third place?
10. Triangular pyramid Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
11. 4s pyramid Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
12. The chord Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
13. 2x cone Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
14. Circle section Equilateral triangle with side 33 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.
15. Trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
16. Cut and cone Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
17. Jewel Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
18. RT - hypotenuse and altitude Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
19. Sequence In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
20. Stock market Simon one day decided to invest € 62000 to the stock market. After six months he invested July 25 stock markets fell by 47%. Fortunately for Simon from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ?

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