# Examples for 8th grade

1. Costume
Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand D
2. Candy
The price for 1kg of more expensive candy is 125 CZK. The price for 1kg of cheaper candy is 100 CZK. We make two different blends of candy. And now. The second blend contains 2kg of more expensive candy and several kg of cheaper candy. The price per 1 kg
3. Fit ball
What is the size of the surface of Gymball (FIT - ball) with a diameter of 65 cm?
4. Digging
A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m X 30m. What is the increase in the level of the plot ?
5. Mr. John
Mr. John wants to buy winter apples Spartan. There are two ways to buy: 1) buy apples at the marketplace, where 1 kg costs 15 CZK. 2) Bring the car to the agricultural farm, where the apples are sold after 9 CZK per kilogram. However, he must pay CZK 150
6. Tiles path
A rectangular park measures 24mX18m. A path 2.4m wide is constructed all around it. Find the cost of paving the path with cement tiles of size 60cm X 40cm at the rate of \$5.60 per tile ?
7. Contestants
In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contesta
8. Class 9A
On the final certificate have one quarter of the class 9A mark "C" of mathematics, seventh mark "C" from the Czech language and two students failed in chemistry. How many students attend class 9A?
9. Two pumps
The first pump fills the tank in 24 hours second pump in another 40 hours. For how long will take fill the tank if operate both pumps at the same time?
10. Cone area and side
Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
11. Cylinder surface area
Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm3. Calculate its surface area.
12. Water reservoir
The water reservoir is filled with one pump for 4 days by the second one for 9 days. Outlet can drain tank in 12 days. How long take fill the reservoir if both pumps are running and not closed outlet channel.
13. Shadow and light
Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
14. Metals
In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
15. 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.
16. Fog
The car started in fog at speed 30 km/h. After a 12-minute drive, the fog dissipated and the driver drove next 12 minutes distance 17 km. On the last 17 km long again the driving conditions deteriorated and the driver drove the speed of 51 km/h. a) Calc
17. Segment in a triangle
In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
18. Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
19. Inscribed circle
XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
20. Conva
How many liters of water fit into the shape of a cylinder with a bottom diameter 20 cm and a height 45 cm?

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