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
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.
Outer perimeter of silo is 24 m. Concrete wall is 18 cm thick. What is diameter and area of inside floor of silo?
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'
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.1 calculate sin(γ)
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 cm2 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.
Surfaces of cubes, one of which has an edge of 18 cm shorter than the other, differ by 7776 mm2. Determine the length of the edges of this cubes.
Calculate radius of the Circumscribed circle in the rectangle with sides 17 and 16. It can be rectangle inscribed by circle?
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 S1=254 cm2 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 dm2 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%.
Rhombus-shaped jewel have area of 86 mm2 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?
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?