# Examples for 8th grade - page 28

1. Journey The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pla
2. RT 11 Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
3. Gauss Help little C.F. Gauss sum all the integers from 1 to 400.
4. Two typists There are two typists who are rewriting the material 814 pages. First can it handle rewrite yourself for 24 days; the second 12 days. First typist wrote material yourself 4 days rest rewrites yourself second typist. How many days will it take rewriting alt
5. Diamond ABCD In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.
6. IS trapezoid Isosceles trapezoid arm measured 35 cm. Height is 30 cm and middle segment is 65 cm. Determine length of its bases.
7. Ice cream in cone In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone.
8. Estate Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
9. Angles in triangle The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
10. Volume and surface Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
11. Carpenter From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
12. Farmer The farmer farming 293 ha of arable land and the remaining 20% are meadows and pastures. How much land farmer owns?
13. Cone in cube The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage.
14. Bridge The bridge arc has a span 34 m and height 3 m. Calculate the radius of the circle arc of this bridge.
15. Reciprocal What is the reciprocal of the sum of the reciprocals of 4 and 9?
16. Mountain railway Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
17. Moon We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
18. Crown Siblings collect a 2-crowns and 5-crowns. Together have 80 coins with a total of value 310 crowns. How many saved two-crowns and how many five-crowns?
19. Internal angles The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
20. Cuboid 5 Calculate the mass of the cuboid with dimensions of 12 cm; 0.8 dm and 100 mm made from spruce wood (density = 550 kg/m3).

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