# Grade - examples - page 48

1. 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?
2. Number train
The numbers 1,2,3,4,5,6,7,8 and 9 traveled by train. The train had three cars and each was carrying just three numbers. No. 1 rode in the first carriage, and in the last carriage was all odd numbers. The conductor calculated sum of the numbers in the first
3. Diagonals
Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
4. Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
5. Classroom 3
How many children are in the classroom, where 13 children are higher than Lenka and 9 children lower than Lenka?
6. 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.
7. 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.
8. Carpenter
From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
9. Farmer
The farmer farming 293 ha of arable land and the remaining 20% are meadows and pastures. How much land farmer owns?
10. Trapezoid - hard example
Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
11. 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.
12. Bridge
The bridge arc has a span 235 m and height 3 m. Calculate the radius of the circle arc of this bridge.
13. 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?
14. 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.
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. 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?
18. 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
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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