# Examples for 9th grade - page 94

1. Rain It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
2. Test points If you earned 80% of the possible 40 points, how many points did you miss to get 100%?
3. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
4. Tangent 3 In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
5. Four poplars Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?
6. Two cities The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B?
7. Lunch Seven classmates go every day for lunch. If they always come to the front in a different order, will be enough school year to take of all the possibilities?
8. Collection of stamps Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
9. Profit per kilo The trader sells apples at a profit of 20% per kilogram. Today, he decided to reduce the price of apples by 10%. How much profit does the trader have today?
10. Trapezium diagonals It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
11. Horizontal distance The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m?
12. Chocolate I have a box of chocolate - white, milk and dark. The ratio of white to milk with dark is 3: 4. The ratio of white and milk to dark is 17: 4. Calculate what is the ratio between white, milk, dark chocolate.
13. Tropical, mild and arctic How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'.
14. Find the 3 Find the distance and mid-point between A(1,2) and B(5,5).
15. Circle described The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
16. Triangular pyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
17. Seawater Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.
18. Digit sum How many are three-digit numbers that have a digit sum of 6?
19. Height as diameter of base The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
20. Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.

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