Examples for 8th grade - page 7
- Prism
Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 15 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube - Slope of track
Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitra (167 m AMSL), if the track is 77 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? - Cone
Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°. - IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm. - Pentagon
Calculate the area of regular pentagon, which diagonal is u=17. - 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? - Railways
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters. - Water
Mix 20 l of water with temperature of 53 °C, 27 l warm of 86 °C and 11 l water of 49 °C. What is the temperature of the mixed water immediately after mixing? - 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. - Mast
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. - Present
Gift box has rectangular shape with dimensions of 10×10×9 cm. Warren wants to cover with square paper with sides of 29 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 - Sea water
Seawater contains about 4.7% salt. How many dm3 of distilled water we must pour into 39 dm3 of sea water to get water with 1.5% salt? - 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? - Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Gear
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears? - Motion
Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. Di - Tare
Gross weight of shipment is 5188 kg and its tare is 5.6%. Calculate the net weight of the shipment.
Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 15 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitra (167 m AMSL), if the track is 77 km long.
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?
Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
Calculate the area of regular pentagon, which diagonal is u=17.
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?
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
Mix 20 l of water with temperature of 53 °C, 27 l warm of 86 °C and 11 l water of 49 °C. What is the temperature of the mixed water immediately after mixing?
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.
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°.
Gift box has rectangular shape with dimensions of 10×10×9 cm. Warren wants to cover with square paper with sides of 29 cm. How much paper left him?
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
Seawater contains about 4.7% salt. How many dm3 of distilled water we must pour into 39 dm3 of sea water to get water with 1.5% salt?
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?
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. Di
Gross weight of shipment is 5188 kg and its tare is 5.6%. Calculate the net weight of the shipment.- «
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