# Examples for 8th grade - page 23

- Horizon

The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - Quadrant II

Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm. - Father and son

Father is three times older than his son. 12 years ago father was nine times older than the son. How old are father and son? - Cone in cylinder

The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage. - Tetrahedral prism

Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm. - Degrees to radians

Convert magnitude of the angle α = 9°39'15" to radians: - Similarity n-gon

9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S_{1}=190 dm^{2}and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm. - Rhombus HP

Calculate area of the rhombus with height 24 dm and perimeter 12 dm. - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]? - Kids

How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge? - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes? - Rectangle

The perimeter of the rectangle is 22 cm and content area 30 cm^{2}. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers. - Two runners

Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi - Tiles

From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles. - Trains for people

It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 19 km, with regular train leave at 5:47 and arrive at 6:13, but train is late and has departure at 9:01 and arrive at 9:25. - Icerink

Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water. - Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm^{3}. Calculate the surface area of the cylinder. - ISO trapezium

Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees. - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 12 cm and u_{2}= 10 cm. Prism height is twice base edge length. - Triangle TBC

TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?

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