# 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? - 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? - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 236 dm. - Rectangle

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

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

Gross weight of shipment is 5073 kg and its tare is 6.9%. Calculate the net weight of the shipment. - Rhombus

It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 6 cm and a_{2}= 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - 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? - 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. - Radians

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

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

Calculate the interior angles at which equilateral rhombus has maximum area. - 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 ?. - Barrel of oil

Barrel of oil weighs 238 kg. When it mold 20% oil, weighed 196 kg. What is the mass of the empty barrel? - 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. - Arc

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

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

How many percent we increase volume and surface of cube, if we magnify its edge by 61%. - Kites

Boys run kite on a cable of 86 meters long. What is the kite altitude, if the angle from the horizontal plane is 77°?

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