# Examples for 7th grade (seventh) - page 3

1. Cube diagonal Determine the length of the cube diagonal with edge 75 mm.
2. Washer Washing machine drum wash at 58 RPM. Washing machine motor pulley has diameter 9 cm. What must be the diameter of the drum machine pulley when the motor is at 438 RPM?
3. Tereza The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
4. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
5. No. of divisors How many different divisors have number ??
6. Motion2 Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?
7. ŽSR Calculate fixed annual personnel costs of operating monorail line 118 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 4-shift operation. Consider the average salary of the employee 885 €.
8. Vinegar 2 How many percentage of getvinegar solution, if we mix to 3.5 liters of 5.8% and 5 liters of 7.6% vinegar?
9. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
10. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
11. Flags How many different flags can be made from colors white, red, green, purple, orange, yellow, blue so that each flag consisted of three different colors?
12. Two cars Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet?
13. Cylinders Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
14. Reverse Pythagorean theorem Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
15. Youth track Youth track from Hronská Dúbrava to Banská Štiavnica which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate size of subsidies to trip group of 28.
16. Compare Compare fractions ?. Which fraction of the lower?
17. It is rectangular? Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
18. Tanks Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
19. Circle arc Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
20. Numbers Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?

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