# Examples for 8th grade - page 10

- Number ratio

Calculate two positive numbers that its ratio is 4:4 and sum was 184. - Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - ISO triangle

Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 128 mm. - Climb in percentage

The height difference between points A and B is 442 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 6.8 km. - Prism

Three cubes are glued into prism, sum of the lengths of all its edges is 259 cm. What is the length of one edge of the original cube? - Profitable bank deposit 2012

Calculate the value of what money lose creditor with a deposit € 7700 for 4 years if the entire duration are interest 2.2% p.a. and tax on interest is 19% and annual inflation is 3.6% (Calculate what you will lose if you leave money lying idle at negative - Hollow sphere

Calculate the weight of a hollow brass sphere (density 8.5 g/cm^{3}), if the outer diameter is 10 cm and wall thickness is 3 mm. - Cube

The cube weighs 47 kg. How weight is cube of the same material, if its dimensions are 3-times smaller? - Equilateral triangle

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 7 mm from it? - Diagonals of the rhombus

Calculate height of rhombus whose diagonals are 15 cm and 5 cm. - Hexagon A

Calculate area of regular hexagon inscribed in circle with radius r=7 m. - 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. - Bicycle wheel

Bicycle wheel has a diameter of 60 cm. Approximately how many times the wheel rotates at 3.7 km long trip? - Tower

How many m^{2}of copper plate should be to replace roof of the tower conical shape with diameter 13 m and the angle at the vertex of the axial section is 150°? - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 35 cm. - Road

Between cities A and B is route 3 km long of rise average 4‰. Calculate the height difference of cities A and B. - 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. - 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? - 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? - Pedestrian up-down hill

Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?

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