# Examples for 7th grade (seventh)

I have homework. The cube has an edge 7 cm long and I must find wall and body diagonal.
2. Pool
Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 8 m, distance of the opposite walls of the pool is 7 m. Estimated depth is 144 cm. How many hectoliters of water consume Mr. Peter to fill the pool
3. Arc
Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
4. Circle
What is the radius of the circle whose perimeter is 6 cm?
5. Number
What number is 20 % smaller than the number 198?
6. Base
Base of building is circle with diameter 25 m. Calculate the circumference of a circular trench witch diameter is 41 cm wider than the diameter of the base.
7. Height UT
How long is height in the equilateral triangle with a side b = 43?
8. Beer
Which beer is better to drink: small beer (0.3 L) for 0.67 € or large (0.5 L) for 1.81 €?
9. Coke
From one ton of coal is produced 772 kg of coke for iron production. How many wagons of coal by 13 tonnes per day is needed for the blast furnace, which has a daily consumption of 1020 tons of coke?
Students of canoeists trip traveled in three days 102 km. Second day traveled 15% more than first day and at the third day 9 km over the second day. How many kilometers traveled each day?
11. Saw
Imagine that the saw blade with diameter 40 cm has one tooth colored with a different color. How long is path describing by the tip of the tooth after 15 minutes, if the blade is rotated 13365 times?
12. Silo
Outer perimeter of silo is 32 m. Concrete wall is 35 cm thick. What is diameter and area of inside floor of silo?
13. Square
Rectangular square has side lengths 183 and 244 meters. How many meters will measure the path that leads straight diagonally from one corner to the other?
14. Cu wire
Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
15. Hop-garden
The length of the rectangular hop garden Mr. Smith increased by 25% and its width by 30%. What is the percentage change in area of hop garden?
16. Divisibility
Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
17. Peleton
Cycling race was run at an average speed of 45 km/h. One cyclist lost with defect 8 minutes. How long and how far he must go at speed 51 km/h to catch peleton again?
18. Cyclist
A cyclist is moving at 35 km/h and follow pedestrian who is walking at speed 4 km/h. Walker has an advantage 19 km. How long take cyclist to catch up with him?
19. Similarity
Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
20. Reciprocal
For given real numbers, calculate reciprocal number.

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