# Examples for 9th grade - page 10

1. Pizza Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated?
2. Triangle SSS Calculate perimeter and area of ​​a triangle ABC, if a=42, b=57 and c=42.
3. Climb On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
4. ISO triangle Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
5. Rotary cone The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
6. Triangular prism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
7. Cone Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
8. Tourists From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 47 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?
9. Shelf How many ways are there to arrange 6 books on a shelf?
10. Diagonals of the rhombus Calculate height of rhombus whose diagonals are 12 cm and 19 cm.
11. Roller Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?
12. Rhombus 2 Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
13. Tower How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
14. Profitable bank deposit 2012 Calculate the value of what money lose creditor with a deposit € 9500 for 4 years if the entire duration are interest 2.6% p.a. and tax on interest is 19% and annual inflation is 3.7% (Calculate what you will lose if you leave money lying idle at negative
15. Equilateral triangle How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
16. Hexagon A Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
17. Ships At 8:40 the ship set sail at 12 km/h. At 19:10 followed by at 29 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took?
18. Similarity coefficient The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
19. Center Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
20. Balls Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.

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