# Grade - examples - page 205

- Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - 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? - 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 - 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? - 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. - Cube root

Find cube root of 18 - 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. - 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? - 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. - 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? - 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? - 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. - Age

In 1960 my age was equal to the digits sum of the year of my birth. What is my age now? - Honza

Honza is 13 years old and Peter 21 years old. After how many years are their ages will be at ratio 7: 9? - 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 - 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? - Equation 15

Solve equation with variables on both sides: - Pamela

Lara Pamela spends her salary of 3000 for food, clothing, recreation and savings, which are in the ratio of 48:20:15:37, respectively. How much does he spend for savings? - 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? - 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.

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