# Examples for 8th grade - page 7

- Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - 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. - Rectangle

Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees. - Radians

Convert 54° to radians. Write result as multiple of number π. - Arc

Circle arc corresponding to angle is 193° is 23 dm long. What is the length of the entire circle? - Cone

Circular cone of height 16 cm and volume 5024 cm^{3}is at third of the height (measured from the bottom) cut plane parallel to base. Calculate the radius and circumference of the circular cut. - Railways

Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters. - Expansion

If one side of the rectangle is larger 3-times and second 4-times, what percentage increases the area of rectangle? - Ravens

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 - Rectangle

In rectangle ABCD with sides |AB|=11, |AD|=12 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?. - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has maximum area. - Tangents

To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre. - Car

Car goes from point A to point B at speed 70 km/h and back 76 km/h. If they goes there and back at speed 73 km/h trip would take 19 minutes shorter. What is distance between points A and B? - Lathe

From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed? - Cu thief

The thief stole 121 meters copper wire with cross-section area of 101 mm^{2.}Calculate how much money gets in the scrap redemption, if redeemed copper for 5.5 eur/kg? The density of copper is 8.96 t/m^{3}. - Described

Calculate perimeter of the circle described by a triangle with sides 418, 59, 430. - Barrel of oil

Barrel of oil weighs 282 kg. When it mold 56% oil, weighed 138 kg. What is the mass of the empty barrel? - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 23 cm and t_{b}=14 cm. - VAT

John paid 1000 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%. - Daily average

Calculate the average temperature during the day, when 14 hours was 20 °C and 10 hours was 15 °C.

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