# Examples for 8th grade - page 61

- Circle section

Equilateral triangle with side 50 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector. - Two runners

Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute - Icerink

Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water. - Silo

Outer perimeter of silo is 24 m. Concrete wall is 18 cm thick. What is diameter and area of inside floor of silo? - 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' - Sines

In ▵ ABC, if sin(α)=0.5 and sin(β)=0.1 calculate sin(γ) - Steamship

Between the two ports on the river is going steamship. The journey there and back takes 14:49. Downstream steamship traveling at 21 km/h, upstream 9 km/h. What is the distance between the ports? - Triangle ABC

Calculate the sides of triangle ABC with area 883 cm^{2}and if a: b: c = 15:7:19 - 2x cone

Circular cone height 60 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone. - Cubes

Surfaces of cubes, one of which has an edge of 18 cm shorter than the other, differ by 7776 mm^{2.}Determine the length of the edges of this cubes. - Circumscription

Calculate radius of the Circumscribed circle in the rectangle with sides 17 and 16. It can be rectangle inscribed by circle? - Box

Calculate the angle between box base 5 x 7 and body diagonal length 14. - Concrete pipe

Concrete pipe is cylindrical with an inner diameter 130 cm and outer 142 cm. Calculate the surface of the concrete pipe, if it is 6 m long. - Magnification of the square

If we increase the square side, increase the content of the 42 %. About what percentage was increased his sides? - Similarity n-gon

11-gones ABCDEFGHIJK and A'B'C'D'E'F'G'H'I'J'K' are similar. The area of 11-gon ABCDEFGHIJK is S_{1}=254 cm^{2}and the diagonal length HG is 20 cm. Calculate area of the 11-gon A'B'C'D'E'F'G'H'I'J'K' if H'G' = 36 cm. - Glass mosaic

How many dm^{2}glass is nessesary to produc 50 slides of a regular 6-gon, whose side has length 7 cm? Assume that cutting glass waste is 14%. - Jewel

Rhombus-shaped jewel have area of 86 mm^{2}and the edge in long 10 mm. Calculate the size of rhombus acute angle. - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 53.7°. Consider a globe with a radius of 6378 km. - How far

From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse? - Failure

Drivers of passenger cars have calculated that at a speed of 60 km/h arrives at destination within 40 minutes. After 20 km refrain five minutes due a technical failure. How fast must go the rest of the way to the finish came at the scheduled time?

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