Examples for 8th grade

Lookout tower
Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m.
A map
A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field?
Two trains
The train runs at speed v1 = 72 km/h. The passenger, sitting in the train, observed that a train long l = 75m in 3 s passed on the other track in the opposite direction. Calculate the speed of this train.
Garden exchange
The garden has the shape of a rectangular trapezoid, the bases of which have dimensions of 60 m and 30 m and a vertical arm of 40 m. The owner exchanged this garden for a parallelogram, the area of which is 7/9 of the area of a trapezoidal garden. What is
Oak trunk
Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³.
Cooker
A current of 2A passes through the immersion cooker at a voltage of 230V. What work do the electric field forces in 2 minutes?
Rectangular land
On a rectangular land with dimensions of 35 m and 18.5 m is a house with a square floor plan with a side of 14 m. What % of the land is not occupied?
Cone from cube
The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m³
Diameter = height
The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
Cannonballs
Of the three cannonballs with a diameter of 16 cm, which landed in the castle courtyard during the battle, the castle blacksmith cast balls with a diameter of 10 cm, which fit into the cannons placed on the walls. How many cannonballs did the blacksmith c
Bricklayers
The first bricklayer would build a wall in 3 days, the second in 4 days. The first bricklayer worked alone for a day, then the second bricklayer came to his aid and they finished the work together. How long did it take to build the wall?
The Earth
The Earth's surface is 510,000,000 km². Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
Wall and body diagonals
The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
Emilio
Emilio made 69 potholders. Each potholder cost him $2.81 to make. If he sells each potholder for $3.12, how much profit will he make?
Similarity of two triangles
The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity)
Clock hands
Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours.
A kite
Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain?
Water mixing
There are 5 liters of water at 75°C in the pot, how much water at 10°C do we have to add to the resulting temperature of 55°C?
The shooter
The shooter heard the impact of the bullet on the target in one second after the shot. The bullet was moving at an average speed of 500 m/s. Calculate with speed of sound of 340 m/s. Determine the distance of the target.
A bucket
A bucket has 4 liters of water in it when it is 2/5 full. How much can it hold?

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