# Grade - examples - page 31

1. Hexagonal prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
2. 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.
3. Minute angle Determine size of angle, which takes minute hand for 75 minutes.
4. Shooter The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
5. Cube The sum of lengths of cube edges is 69 cm. What is its surface and volume?
6. Wiring Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 \$mm2?
7. Mystery of stereometrie Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
8. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
9. Pumps Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
10. Compass What angle are between directions WSW (WestSouthWest) and SSE (SouthSouthEast) on the compass?
11. Sphere and cone Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
12. 3y inflation Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll.
13. Lock Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
14. Side c In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
15. Pit Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when w
16. Ratio Increase in the ratio 20:4 number 18.5.
17. Black building Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin
18. Road Average climb of the road is given by ratio 1:15. By what angle road average climb?
19. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
20. Circle From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.

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