# Grade - examples - page 106

1. 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.
2. Highway
Six trucks will be used to build the roadside 18 days. After 3 days, two more trucks were sent to build. How long will it take for material move?
3. Trinity
How many different triads can be selected from the group 43 students?
4. Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille.
5. Tmp workers
Three temporary workers cleaned 60 m of walkway in 5 hours. How many meters of the walkway cleared seven volunteers for eight hours?
6. Roof 7
The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
7. Minute
Two boys started from one place. First went north at velocity 3 m/s and the second to the east with velocity 4 m/s. How far apart they are after minute?
8. Grass garden
Mr. Grass would itself be mowed garden for 5 hours. His son Michael could do it for 7 hours. They agreed that they wake up at 5 am and begins to mow together. Ms. Grass needs drive into town at 8.30. Michael says that at that time they're done with work..
9. Repairman
Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker?
10. Candies
There are two types of candies in the store at 20 CZK/kg and 80 CZK/kg. How much will be cost a mix if we mix 22kg cheaper and 4kg more expensive candies?
11. Sum on dice
We have two dice. What is the greater likelihood of fall a total sum 7 or 8 ? (write 7, 8 or 0 if the probabilities are the same)?
12. Surface area
Calculate the surface area of a four-sides 2-m high prism which base is a rectangle with sides 17 cm and 1.3 dm
13. Water reservoir
The water tank has a cuboid with edges a= 1 m, b=2 m , c = 1 m. Calculate how many centimeters of water level falls, if we fill fifteen 12 liters cans.
14. Rhumbline
Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.
15. Rectangle from string
String 12m. Make rectangle when one side is two times longer than its width.
16. Matches
George poured out of the box matches and composing them triangles and no match was left. Then he tries squares, hexagons and octagons and no match was left. How many matches must be at least in the box?
17. Tank
The tank bottom has dimensions of 1.5 m and 3 2/6 m. The tank is 459.1 hl of water. How high is the water surface?
18. Journey to grandma
Daniel traveled to grandma. He travel 100 km along. Halfway travel by train, one quarter by bus, one tenth by the bicycle and the rest travel by car. How many km travel km by car?
19. The chord
Calculate a chord length which the distance from the center of the circle (S, 6 cm) equals 3 cm.
20. Truncated cone
A truncated cone has a bases radiuses 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume.

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