# Examples for 8th grade - page 6

- Water

Mix 68 l of water with temperature of 87 °C, 17 l warm of 42 °C and 55 l water of 50 °C. What is the temperature of the mixed water immediately after mixing? - Slope of track

Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long. - Cyclist

Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane? - Climb in percentage

The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km. - Right triangle

Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle. - Spherical cap

From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere? - Pentagon

Calculate the area of regular pentagon, which diagonal is u=17. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Present

Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him? - Mast

Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'. - Sea water

Seawater contains about 4.3% salt. How many dm^{3}of distilled water we must pour into 5 dm^{3}of sea water to get water with 1.8% salt? - Pediatrician

Pediatrician this month of 20 working days takes 4 days holidays. What is the probability that on Monday will be at work? - Road repair

Road repair took 10 days for 36 workers if they worked 9 hours a day. How many days take repair same road 37 workers if they work 8 per day? - Barrel of oil

Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel? - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Engineer Kažimír

The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri - Cube zoom

How many percent we increase volume and surface of cube, if we magnify its edge by 38%. - Rectangle - sides ratio

Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673. - Rhombus and inscribed circle

It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals. - Car

Car goes from point A to point B at speed 86 km/h and back 53 km/h. If they goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is distance between points A and B?

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