# Examples for 8th grade - page 30

- Arc

The length of the circle is 33 amd arc length of the circle 11. What is the magnitude of the angle of this arc? - Map 2

At what scale is made map if the distance 6.8 km corresponds on the map segment 4 cm long? - Painters

First painter painted fence himself for 12 hours, the second painter 3 hours sooner than first, and the third painters slowest up to 20 hours. How long took them paint fence if worked together? - Building base

Excavation for the building base is 350x600x26000. Calculate its volume in m^{3.} - Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm^{2.}Determine the area of the trapezoid A - Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Skier

At this point, the first skier lead 14 km before the second skier and travels at a constant speed 13 km/h. The second skier rides at 19 km/h. How long take him to catch up the first? - Circumference - a simple

What is the ratio of the circumference of any circle and its diameter? Write the result as a real number rounded to 2 decimal places. - Swing

A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance? - Mountain railway

Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track. - Cuboids in cube

How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters? - Paul and Honza

Honza went to chat on a bike without a break 3.0 hours. Paul the same way without breaks 30 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not. - Retail

At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 3.9% of weight of the goods and retail still have a profit of 13.2%? Goods are sold at retail for 17 euro per kg. - Triangle

Calculate heights of the triangle ABC if sides of the triangle are a=48, b=81 and c=98. - The professor's birthday

Professor of mathematics had 48 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc - VAT

VAT is a tax which the state artificially betrays goods and services for final consumption. VAT in Slovakia is 20%. Calculate how much percent pay less tax residents of Switzerland, when VAT is only 8%. - Gasholder

The gasholder has spherical shape with a diameter 23 m. How many m^{3}can hold in? - Jan

Jan is 13 years and Peter 21 years old. For how many years will their ages in the ratio of 7:9? - Password

The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9. I - Carbon dioxide

Calculate how many grams of oxygen are in 126 g of carbon dioxide CO_{2}. Relative atomic mass of oxygen is 16 and of carbon is 12.

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