# Examples for 8th grade - page 52

- Cube from sphere

What largest surface area (in cm^{2}) can have a cube that was cut out of a sphere with radius 43 cm? - Profits

Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn? - Wheel

What is the wheel diameter if on the 0.37 km track turns 112 times? - Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - Two trains meet

From A started at 7:15 express train at speed 85 km/h to B. From B started passenger train at 8:30 in the direction to A and at speed 55 km/h. The distance A and B is 386 1/4 km. At what time and at what distance from B the two trains meet? - Legs

In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people? - Scouts

Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type? - Tiler

On what surface m^{2}tiler must lay 30 square tiles, each of which has a side 25 cm? - Parachutists

Parachutists during freefall firstly held in groups of 4, then of 6, then 9, 12 and finally of 18 members. How many parachutists jump at least should be, if at each group must all be involved. - Alfa, beta, gama

In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC. - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Solution

What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture? - Eva

When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet? - Three workers

Three workers were rewarded CZK 9200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received? - Complementary angles

Two angles are complementary. If one angle measures 10°, what is the measure of the second angle? - MATES

In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is? - Percent

From 99 children who participated in the ski course were 23 excellent skiers, 13 good and 20 average and the rest were beginners. Calculate this data in percentages. - Cars speeds

Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes? - Two months

Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies? - Crown coins

Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?

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