# Units - problems - page 29

1. 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.
2. 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?
3. Stones in aquarium
In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
4. Diagonals
Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
5. 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.
6. Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
7. Carpenter
From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
8. Honza + Alice + Tonda
Honza + Alice + Tonda have a total of 111 USD. The ratio between Honza and Alena is 5:6 and the ratio between Alice and Tonda is 4:5 How many money have each of them?
9. 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.
10. 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.
11. 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).
12. Car
The driver of a car is to get to 608 km distant city. From atlas found that 162 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 116 km/h. Calculate how many hours it will t
13. Coin
How many 50-cent coins must be put in a row that next 50-cent coins after them (above) rolled on it axis?
14. 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
15. JUDr. Usury
Judge JUDr. Usury approved the agreement on guilt and punishment where confessed to pay daily interest 0.18%. How big is a yearly interest? Year has 360 days.
16. Apples
Mr. Vesely give to the market his own 48 kg of apples, 40 kg from Mr. Kovar and 72 kg of Mr. Novak. Grossed a total of 1,920 CZK. How must divide income money for apples?
17. Two diggers
There are two diggers. One digger digs a pit 46 hours second gidding 2 times faster. a) how long took to dig a pit second digger b) how long took dig together
18. Tourist Jirka
Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
19. Bomber
Bomber flies 10 km at 600 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s2.
20. Lorry
The lorry was loaded with 18 boxes of 15 kg. How many boxes with weight 18 kg can be loaded, if total load must be same?

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