# Grade - examples - page 19

1. 4side pyramid Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
2. Square diagonal Calculate the length of diagonal of the square with side a = 23 cm.
3. Freedom In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number.
4. LCM What is the least common multiple of 36, 44, 21?
5. Triangles Equilateral triangle with side 40 cm has the same perimeter as an isosceles triangle with arm of 45 cm. Calculate the base x of an isosceles triangle.
6. Vinegar We must dilute 16 liters of 8.8% aqueous vinegar to 4.1% one. How much water is necessary to add?
7. Rabbits In the hutch are 48 mottled rabbits. Brown are 23 less than mottled and white are 8-times less than mottled. How many rabbits are in the hutch?
8. Map On the tourist map at a scale of 1 : 50000 is distance between two points along a straight road 3.7 cm. How long travels this distance on a bike at 30 km/h? Time express in minutes.
9. Clocks How long path will walk the end of the clock's minute-hand long 7 cm for 330 minutes? How long will walk in the same time hour-hand?
10. OK circle Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
11. Expression If it is true that ? is:
12. Triangle ABC Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
13. Roman numerals Write numbers written in Roman numerals as decimal.
14. Pumps The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
16. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
17. Trains From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains.
18. Pyramid a+h Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
19. Prism Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
20. Wire One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?

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