Examples for 8th grade - page 20
- Count of roots
How many solutions has equation x. y = 2531 with two unknowns on the set of natural numbers?
- Similarity n-gon
11-gones ABCDEFGHIJK and A'B'C'D'E'F'G'H'I'J'K' are similar. The area of 11-gon ABCDEFGHIJK is S1=254 cm2 and the diagonal length HG is 20 cm. Calculate area of the 11-gon A'B'C'D'E'F'G'H'I'J'K' if H'G' = 36 cm.
- Cone in cylinder
The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage.
- Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
Man goes with a dog on a long walk 18 km from the house. Man is walking at speed 5.3 km/h and a dog that constantly running between house and man at 17.1 km/h. How many kilometers will run the dog when they reach their destination?
- Christmas Day
In leap years was 53 Sundays. On what day of the week fell to Christmas Day?
- Rhombus HP
Calculate area of the rhombus with height 98 mm and perimeter 20 mm.
The owner of the house is insured against natural disasters and pays 0.04% annually of the value of house 103 Eur. Calculate the value of the house. Calculate the probability of disaster, if you know that 42% of the insurance is to pay damages.
Workers digging a jump pit in the school yard. Pit has a cuboid shape with a length 20 m, a width 20 dm and depth 36 cm. They excavate 0.4 cubic meters of soil an hour. How much time (hours and minutes) is need to the excavate this pit?
- Reservoir + water
Reservoir completely filled with water weighs 13 kg. After pouring off three quarters of the amount of water weights 4 kg. Calculate the weight and volume of the reservoir.
Calculate height of the equilateral triangle if its perimeter is 54?
- Electronics: Resistors in parallel
From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 8kΩ a R2 = 18kΩ
The perimeter of a circular sector with an angle 2 rad is 53 cm. Determine the radius of the circle from which the sector comes.
- Degrees to radians
Convert magnitude of the angle α = 618°40'29" to radians:
- Concrete pipe
Concrete pipe is cylindrical with an inner diameter 130 cm and outer 142 cm. Calculate the surface of the concrete pipe, if it is 6 m long.
The top of a lighthouse is 12 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
Area of circle inscribed in a square is 6. What is the area of a circle circumscribed around a square?
- Cathethus and the inscribed circle
In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
I have homework. The cube has an edge 11 cm long and I must find wall and body diagonal.
Clerk got to pay 1200 Euros in banknotes of 50 and 200 Eur. Total got 9 banknotes. How many was which?