# Examples for 9th grade - page 101

1. Sphere floating Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
2. Spherical cap 4 What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
3. Square metal sheet Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet. Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
5. Castle tower The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap.
6. Right triangular prism We have cuboid with a base and dimensions of 12 cm and 5 cm and height of 4 cm. The tablecloth cut it into two identical triangular prisms with right triangular bases. The surface of the created prisms was painted with color. Calculate the surface area of.
7. Isosceles trapezoid The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?
8. The larger The larger of two numbers is nine more than four times the smaller number. The sum of the two numbers is fifty-nine. Find the two numbers.
9. Land Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
10. The diagram 2 The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
11. Cube root Find cube root of 18
12. Age In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
13. Oranges Mother divided her three children's oranges in a ratio of 6:5:4. Two children gave 45 oranges. How many oranges were there?
14. Square sides If the square side increases by 28%, the square circumference increases by 11.2 meters. Find the length of the original square side.
15. Apples Zuzana bought 3 kg Jonathan apples. Then she noticed that Golden apples were 3 CZK a kilogram cheaper. So they bought 2 kg. For apples, she paid a total of CZK 109. How much did 1 kg Jonathan and how much Golden?
16. Mushrooms Grandfather gathered fresh mushrooms. The fifth was wormwood, and it was thrown away, the other dried up. He obtained 720 grams of dried mushrooms. How many kilograms did the grandfather collect, and by drying the mushrooms they lost 75% of their weight?
17. Honza Honza is 13 years old and Peter 21 years old. After how many years are their ages will be at ratio 7: 9?
18. The cube The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?
19. Bottles The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
20. Glass with icecream We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be?

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