# Examples for 9th grade - page 12

1. Cuboid Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
2. Square diagonal Calculate the length of diagonal of the square with side a = 23 cm.
3. 4side pyramid Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
4. 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.
5. 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.
6. 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?
7. OK circle Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
8. 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.
9. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
10. 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.
11. Pyramid a+h Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
12. 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.
13. Wire One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?
14. n-gon II What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
15. Canopy Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
16. Pentagon Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
17. Rectangles How many rectangles with area 8713 cm2 whose sides is natural numbers are?
18. Estate Semicircle estate must be fence. The straight section has 26 meters long fence. How many meters of fence should buy?
19. n-gon Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
20. Stairway What angle rising stairway if step height in 17 cm and width 27 cm?

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