# Examples for 8th grade - page 13

1. Parallelogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
2. Octahedron - sum On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
3. Cubes Cube, which consists of 27 small cubes with edge 4 dm has volume:
4. 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°
5. 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.
6. Square diagonal Calculate the length of diagonal of the square with side a = 23 cm.
7. Two doctors Doctor A will determine the correct diagnosis with a probability 86% and doctor B with a probability 86%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.
8. Vinegar We must dilute 16 liters of 8.8% aqueous vinegar to 4.1% one. How much water is necessary to add?
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. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
12. Road embankment 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?
13. Pyramid a+h Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
14. 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.
15. Crossroads The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
16. Wire One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?
17. n-gon II What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
18. 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?
19. Percent calculation Calculate 61% if 85% is 38.
20. 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.

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