# Examples for 9th grade - page 14

- Balls

Ping pong balls have a diameter of approximately 4.6 cm. They are sold in boxes of 4 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w - Discounts on rail (ZSSK)

The railway company ZSSK offers a discount of 15% (REGIONAL) for 5 Eur/year. Calculate the real discount rate as a percentage, where passengers will travel 19 Eur per week. - Slope

What is the slope of a line with an inclination -221°? - Accidents

The count of accidents in 1995 caused 8780 women which is 8.4%. How many men caused the accidents? - Cylinder - A&V

The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder? - Steeple

Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high? - Playing cards

How many possible ways are to shuffle 7 playing cards? - KLMN

In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN. - Barrel 3

Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel? - Posters

Column with posters in the form of a cylinder is 2 m high and its diameter is 1.7 m. What is the content area for which it is possible to stick posters? - Sugar - cuboid

Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet i - Pyramid

Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges. - Free fall

Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s^{2} - Cylinder - h

Cylinder volume is 215 cm^{3}. Base radius is 2 cm. Calculate the height of the cylinder. - n-gon

What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm? - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - Reservoir + water

Reservoir completely filled with water weighs 12 kg. After pouring off three quarters of the amount of water weights 3 kg. Calculate the weight and volume of the reservoir. - Truncated cone

Calculate the height of the rotating truncated cone with volume V = 1115 cm^{3}and a base radii r_{1}= 7.9 cm and r_{2}= 9.7 cm. - Greek railwayman

Wesley works for the Slovak railways since 1986. His salary is 864 €. His colleague, Evgenias works in the Greek State Railways from 1991. Earns 5010 € per month. Calculate how many hours a day must Evgenias work to earn as much as Wesley and if they w - Right triangle

Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm.

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