Examples for 8th grade - page 6
- 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?
Calculate the area of regular pentagon, which diagonal is u=14.
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?
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'
- 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
The areas of the two circles are in the ratio 1:15. The larger circle has diameter 25. Calculate the radius of the smaller circle.
- 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?
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
- 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.
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″.
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'.
Gross weight of shipment is 5073 kg and its tare is 6.9%. Calculate the net weight of the shipment.
- IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 26 cm, c = |CD| = 5 cm and legs b = d = |BC| = |AD| = 19 cm.
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?
On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together?
Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears?
Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
Circular cone of height 16 cm and volume 5024 cm3 is at third of the height (measured from the bottom) cut plane parallel to base. Calculate the radius and circumference of the circular cut.
The tale of the Seven Ravens were seven brothers, each of whom was born exactly 1.5 years after the previous one. When the eldest of the brothers was 4-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur