# Examples for 9th grade - page 28

- Square

If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm^{2.}Determine the side length of the original square. - 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? - 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? - 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. - 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. - 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? - 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. - 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. - 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 - 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 - Gasholder

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

Write the first 7 members of an arithmetic sequence: a_{1}=8, d=-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 - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface. - ISO trapezoid v2

bases of Isosceles trapezoid measured 12 cm and 2 cm and its perimeter is 18 cm. What is the are of a trapezoid? - ISO Triangle V2

Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle. - Examination

The class is 22 students. How many ways can choose four to examination? - Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm^{2.}

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