# Examples for 8th grade - page 48

1. Polygon 42 Which polygon has 42 more diagonals than sides?
2. Area of the cone Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
3. Reciprocal It is true (prove it) that if a> b> 0: ?
4. Train expres At 8.00 strarted from Bratislava to Poprad express Tatry. Cities are distant 340 kilometers. At the same time started from Poprad express Danube to Bratislava. Express Tatry's average speed is 80 km/h, Danube 90 km/h. At what distance from Poprad trains w
5. Angles The outer angle of the triangle ABC at the vertex A is 114°12'. The outer angle at the vertex B is 139°18'. What size is the internal angle at the vertex C?
6. Saw Imagine that the saw blade with diameter 40 cm has one tooth colored with a different color. How long is path describing by the tip of the tooth after 15 minutes, if the blade is rotated 13365 times?
7. Trapezoid thirds The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
8. Antennas If you give me two antennas will be same. If you give me again your two antenna I have a 5× so many than you. How many antennas have both mans?
9. Otto and Joachim Otto and Joachim go through the woods. After some time Otto tire and make 15 minutes stop. Joachim meanwhile continues at 5 km/h. Otto when he set off again, first running speed of 7 km/h, but it keep only 30 sec and 1 minute must continue at 3 km/h. This.
10. Chimney Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney.
11. Right triangle trigonometrics Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
12. Distance runner Distance runner already climbed three fifths of the total route. Thus passed 90 km. How many km he have to stop? How long is his route?
13. Three piles 100 kg of sugar we divide into three piles. The first pile is small. If we added to second 2 kg of sugar it would have 25% more sugar than the first pile. If we added to third pile 3 kg of sugar it would have 20% more sugar than the 2nd pile. How many kil
14. Hexa prism Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
15. Determine the number Determine the number x that ?.
16. Rectangles - sides One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?
17. Truck PRG-BA Truck driving on highway from Prague to Bratislava at average speed of 72 km/h. At the moment when the truck passes 54 kilometer from Prague passenger car departs from Prague which travel to Bratislava at speed 90 km/h. When and where (at waht highway ki
18. Two numbers The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.
19. Diplomas Suzanne helped write out diplomas. Issuance its first took 3 minutes, each next 2.3 minutes. How much time it will take to write out n=16 diplomas (including the first), write out this pace?
20. Cottages The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three?

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