# Examples for 8th grade - page 7

- Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees. - Alcohol

How many 46% alcohol we need to pour into 3 liters 63% alcohol to get p3% of the alcohol? How many 52% alcohol we get? - Above 100%

What is 155% of 210? - Slope of track

Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long. - Cyclist

Cyclist goes uphill 1 km for 6.3 minutes and downhill minutes for 2.1 minutes, both applied to the pedals same force. How long he pass 1 km by plane? - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Pentagon

Calculate the area of regular pentagon, which diagonal is u=14. - Spherical cap

From the sphere of radius 12 was truncated spherical cap. Its height is 4. What part of the volume is spherical cap from whole sphere? - Cone

Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″. - IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 39 cm, c = |CD| = 8 cm and legs b = d = |BC| = |AD| = 24 cm. - Right triangle

Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle. - Mast

Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'. - Water

Mix 61 l of water with temperature of 48 °C, 58 l warm of 57 °C and 47 l water of 39 °C. What is the temperature of the mixed water immediately after mixing? - Present

Gift box has rectangular shape with dimensions of 4×9×19 cm. Todd wants to cover with square paper with sides of 27 cm. How much paper left him? - 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 - Railways

Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters. - Sea water

Seawater contains about 7% salt. How many dm^{3}of distilled water we must pour into 14 dm^{3}of sea water to get water with 1.7% salt? - Road repair

Road repair took 16 days for 34 workers if they worked 6 hours a day. How many days take repair same road 33 workers if they work 6 per day? - Motion

Cyclist started at 5:00 from point N to point O. After 20 minutes, followed him at the same speed the second cyclist. Walker, which went from O to N, started at 5:40. After 56 minutes he met the first cyclist and after next 16 minutes the second cyclist. D - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears?

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