Examples for 8th grade - page 22

Rhombus HP
Calculate area of the rhombus with height 24 dm and perimeter 12 dm.
Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm². Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
Oil rig
Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
Two runners
Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi
Tiles
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
Baker
The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough?
Trains for people
It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 85 km, with regular train leave at 7:00 and arrive at 8:18, but train is late and has departure at 8:10 and arrive at 9:27.
Icerink
Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water.
Rhombus base
Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 12 cm and u₂ = 10 cm. Prism height is twice base edge length.
ISO trapezium
Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
Certificate
There is 31 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 2. How many students have mark 1 and how many mark 2?
Triangle TBC
TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
Truncated pyramid
How many cubic meters is volume of a regular four-side truncated pyramid with edges one meter and 60 cm and high 250 mm?
Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m³. Calculate the volume, surface and diameter of the sphere.
Pine wood
From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum
Apartments
Apartment on the first floor was 10% more expensive than the same apartment on the second floor. The difference was 105 Kc annually. Calculate the annual rent of the apartment in the first floor and from apartment on the second floor.
Concrete pipe
Concrete pipe is cylindrical with an inner diameter 110 cm and outer 120 cm. Calculate the surface of the concrete pipe, if it is 9 m long.
Map - climb
On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m. What is average angle of climb of this cable car track?
Sphere - parts
Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
Perpendicular
Determine the slope of the line perpendicular to the line p: y = -x +4.

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