# Examples for 7th grade (seventh)

1. Thales Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole.
2. Display case Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs.
3. 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?
4. Rhombus EFGH Construct the rhombus EFGH where e = 6.7cm, height to side h: vh = 5cm
5. Metal pyramid Find the weight of a regular quadrilateral pyramid with a 5 cm length and 6,5 cm body height is made from material with density g/cm3.
6. Father and son Father is 48 years old, son 23. When will be the father twice older than a son?
7. Diameter What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
8. Flowerbed In the park there is a large circular flowerbed with a diameter of 12 m. Jakub circulated him ten times and the smaller Vojtoseven times. How many meters each went by and how many meters did Jakub run more than Vojta?
9. Force meter We put the statuette on the force meter. The force meter showed a value 25 N. Then we placed the statuette on the force meter completely immersed in the water. The force meter showed a value 17 N. What is the volume of the statuette?
10. Juice box The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?
11. The tank The tank has 1320 liters of water. The tank has the shape of a prism, its base is an rectangle with sides a = 0,6 m and b = 1,5 m. How high does the water level reach in the tank?
12. Fewer than 500 sheep, There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain. But they can stand in the seventh order. How many are sheep?
13. Cremons The freight wagon is shaped like cuboid 21m and 3.5m and 4.2m How many cremons can be loaded if one is a cube with an edge length of 7 cm?
14. LCD 2 The least common denominator of 2/5, 1/2, and 3/4
15. Children pool The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film
16. Highway Six trucks will be used to build the roadside 18 days. After 3 days, two more trucks were sent to build. How long will it take for material move?
17. Stones in aquarium In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
18. Czech crown salary The monthly salary of the employee is CZK 10,800. In the course of the year the bulk salary increased by CZK 500. Calculate which month (1 ... 12) was increased if its annual income was 133,600 CZK.
19. Annulus The radius of the larger circle is 8cm, the radius of smaller is 5cm. Calculate the contents of the annulus.
20. Four circles 1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.

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