# Examples for 8th grade - page 15

- Train

A passenger train traveled for 4 hours 136 km. 2.7 hours after its departure started fast train and caught it on 324 km. How many km/h is different its average speeds? - Wire D

Wire length 5 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle. - 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. - Lead cube

Calculate the edge of the cube made from lead, which weighs 11 kg. The density of lead is 11341 kg/m^{3.} - Parquet floor

Three workers laid parquet floor for 1.957 hour. The first one would do this work alone 5 hours, the second in 9 hours. For how many hours would fulfill this work the third worker, if he worked alone? - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Rhombus

Internal angles of rhombus is in ratio 3:6. How many times is the shorter diagonal longer than side of rhombus? - Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 6 so that it is divided into three parts in the ratio 3:2:5. Calculate the circumference of the triangle ABC. - Cylinder - h

Cylinder volume is 129 cm^{3.}Base radius is 3 cm. Calculate the height of the cylinder. - Wood in the forest

The amount of wood in the forest was estimated at 24000 m^{3.}How much wood will be in forest after 3 years if the annual growth of wood is 3% each year and logging 360 m^{3}each year? - Slope

What is the slope of a line with an inclination 52°? - Stock market

Simon one day decided to invest € 88000 to the stock market. After six months he invested July 5 stock markets fell by 56%. Fortunately for Simon from July 5 5 to October 5 his shares have risen by 39%. Simon is then: ? - Prism

The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism? - Cyclists

Cyclist who rides at an average speed 17 km/h travels trip distance 14 min before the cyclist who rides at an average speed 15 km/h. What is the length of this cyclist trip(distance in km)? - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Division

Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 1:6:3. How many candies should each get if in bag were 210? - Magnification of the square

If we increase the square side, increase the content of the 42 %. About what percentage was increased his sides? - Crossroads

The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car. - Rotating cone II

Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm. - Playing cards

How many possible ways are to shuffle 7 playing cards?

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