# Examples for secondary school students - page 71

1. Sss triangle Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
2. Microorganisms The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.
3. Height of the room Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
4. Perimeter of RT Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
5. 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. )
6. Spherical cap 4 What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
7. 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?
8. 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
9. 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.
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. Age In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
12. 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?
13. 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?
14. Sum of two primes Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
15. Three numbers We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
16. A man 2 A man divides \$10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.
17. KLM triangle Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
18. Employees There are 1116 people working in three factory halls. In the first one, there are 18% more than the third, and 60 persons more than the second. How many employees work in individual halls?
19. 75th percentile (quartille Q3) Find 75th percentile for 30,42,42,46,46,46,50,50,54
20. Free fall The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.

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