# Examples for 7th grade (seventh)

1. Sputnik
The first Earth satellite was flying at speed 8000 m/s. At that rate he circled the earth in 82 minutes. Jet flies at an average speed 800 km/h. How long would it take circle the earth round?
2. Cylindrical tank
Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
3. Tree shadow 3
What is the diameter of a tree around which is 3m 9dm 7cm long rope wrapped? How big is its cross-sectional area?
4. Price increase
A 20 percent price increase meant a 90-crown raise. How many cost a product after?
5. Collection
John has collected half a bucket of raspberries in 45 minutes, Eva collects the whole bucket in an hour. How many minutes it would take to fill a bucket if the two children work together?
6. Rectangle
The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
7. Loading car
The car was loaded with 78 boxes weighing 19 kg. How many 25kg boxes can load if the total weight is the same?
8. Magic number
The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
9. Candies
The price for 1 kg of more expensive candies is 125 CZK. The price for 1 kg of cheaper candy is 100 CZK. We mix two different mixtures of candy. A) The first mixture contains 2 kg more expensive and 0.5 kg cheaper candy. Calculate the price for 1 kg of
10. Unknown number
Determine the unknown number that is equal to a quarter of the fifth of number, which is by 152 more than unknown number.
11. Cylinder twice
If the radius of the cylinder increases twice, and the height is reduced twice, then the volume of the cylinder increases (how many times?):
12. Prism
Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
13. Engine pulley
The engine has a 1460 rev / min (RPM). Disc diameter is 350 mm. What will be the disc peripheral speed in RPM? Pulleys on the engine has diameter 80mm, on a disc has diameter 160mm.
14. Copper plate
Calculate the thickness of the copper plate with a density 8.7 g/cm³ measuring 1.5 meters and 80 cm and its weight is 3.65 kg
15. Ratios
Reduce the numbers: 50 in a 1:2 ratio 111 at a ratio of 2:3 70 at 10:50 560 at a ratio of 3:8
16. Call of Duty
Game Call of Duty in CTF (Capture the Flag) opposes the British and the Germans, whose bases are 15 km apart. A German soldier stole the British flag and hid it with it in a secret place between the bases. If the British soldiers set out at a speed of 14
17. Cube
Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
18. Donuts
In the dining room at one table sit Thomas, Filip and Martin. Together they eat 36 donuts. How many donuts eaten everyone, when Filip ate twice as much as Thomas and Martin even half over Filip?
19. Cuboid - volume, diagonals
The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
20. Bar
Half of the bar is green, the third is yellow and the remaining 40cm is red. How long is a bar?

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