# Grade - examples - page 204

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. Water lilies
Water lilies are growing on the pond and their number is doubled every day. The whole layer is covered in 12 days. How many days will it cover 8 layers?
4. 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.
5. Expression plus minus
Evaluate expression: (-1)2 . 12 – 6 : 3 + (-3) . (-2) + 22 – (-3) . 2
6. Mixed numbers
Rewrite mixed numbers so the fractions have the same denominator: 5 1/5 - 2 2/3
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.
8. 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.
9. Infinite sum of areas
Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
10. Tickets
On Monday, 33 tickets were sold. Every next day, twice as many as the previous day. How many tickets were sold on Friday and how many totally from Monday to Friday?
11. 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?
12. Isosceles triangle
The circumference of the isosceles triangle is 32.5 dm. Base length is 153 cm. How long is the leg of this triangle?
13. 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.
14. 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.
15. 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?
16. 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
17. Cube root
Find cube root of 18
18. 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?
19. Dort
The cube-shaped cube box has the dimensions of 30 cm × 30 cm × 12 cm. How many CZK (Czech crowns) would cost be the biggest cake that would fit into the box when a 10 cm³ cake costs CZK 0.5? The cake has the same shape as the box.
20. Twins with friend
The twins Danka and Janka went to the cinema with their friend Betka. Only six seats in the second row were available in the cinema. How many do they may sit, if the twins want to sit next to each other, Danka always to the right of Janka and Betka near on

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