Examples for 8th grade - page 15
- The chord
Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
- Required reserves
Calculate what is the minimum amount of money that bank must hold in cash from your deposit 2750 Eur. How much money is ideally created in the banking system from your deposit if the level of minimum reserve requirement is 2.15%? Consider fractional re
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
The base of the prism is a rhombus with a side 30 cm and height 27 cm. The height of the prism is 180% longer than the side length of the rhombus. Calculate the volume of the prism.
- Painter Pavel
Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.
What is the slope of a line with an inclination -221°?
- Cylinder - A&V
The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
- Tea blend
Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k
- 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
Column with posters in the form of a cylinder is 2.4 m high and its diameter is 2.5 m. What is the content area for which it is possible to stick posters?
- Square grid
Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
On double track line between stations K and M went against each other two trains. The first train passed the distance between stations for 3.5 hours, the second, which had an average speed of 12 km/h more passed for 3.05 hours. Calculate the distance betw
- 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
- Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
- Stock market
Simon one day decided to invest € 69000 to the stock market. After six months he invested July 19 stock markets fell by 55%. Fortunately for Simon from July 19 5 to October 19 his shares have risen by 19%. Simon is then: ?
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.
What is the side length of the regular 5-gon inscribed in a circle of radius 12 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.
- Wood in the forest
The amount of wood in the forest was estimated at 7000 m3. How much wood will be in forest after 2 years if the annual growth of wood is 2.2% each year and logging 70 m3 each year?