# Examples for 8th grade - page 11

- Team

The football team has 11 players. Their average age is 21 years. During the match due to injury, one player withdraws and the average age of the team is 20. How old was injured player? - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 236 dm. - Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 7 cm. - Radius

Determine the radius of the circle, if its perimeter and area is the same number. - Tinsmith

Tinsmith construct chimney pipe 126 cm long and 11 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add $x cm width of the plate? - Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 50 degrees, |AB| = 5 cm. Calculate the volume of the prism. - Hole

In the center of the cube with edge 15 cm we will drill cylinder shape hole. Volume of the hole must be 28% of the cube. What drill diameter should be chosen? - Cu wire

Copper wire has a length l = 210 m and diameter d = 10 mm. Calculate the weight if density of copper is ρ = 8500 kg/m^{3.}Result round to one decimal place. - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle. - Discount

Product has been discounted twice by 14%. What is the total discount given? - Balls

Three metal balls with volumes V_{1}=41 cm^{3}V_{2}=58 cm^{3}and V_{3}=83 cm^{3}melted into one ball. Determine it's surface area. - Air

Room is 26.2 m long, 23.4 dm wide and 628 cm high. How many people can simultaneously be in this room if for hygiene reasons is calculated 5100 dm^{3}of air per person? - Tourists

From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 39 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group? - Shelf

How many ways are there to arrange 9 books on a shelf? - Cuboid

Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60° - Diofant 2

Is equation ? solvable on the set of integers Z? - Clocks

How long path will walk the end of the clock's minute-hand long 24 cm for 110 minutes? How long will walk in the same time hour-hand? - Building

How high is the building that throws horizontal shadow 58.5 m long at angle 36°36'? - Square diagonal

Calculate the length of diagonal of the square with side a = 18 cm. - Cubes

Cube, which consists of 27 small cubes with edge 3 dm has volume:

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