# Examples for 8th grade - page 8

- Tare

Gross weight of shipment is 5188 kg and its tare is 5.6%. Calculate the net weight of the shipment. - Maximum area of rhombus

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

Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears? - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm. - Motion

Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. Di - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Rectangle

In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?. - Expansion

If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle? - Daily average

Calculate the average temperature during the day, when 13 hours was 22 °C and 11 hours was 17 °C. - Tangents

To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. - Radians

Convert 270° to radians. Write result as multiple of number π. - Sea water

Mixing 34 kg of sea water with 34 kg rainwater is created water containing 3.4% salt. How many percent sea water contains salt? - Lathe

From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed? - Cu thief

The thief stole 122 meters copper wire with cross-section area of 95 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}. - Arc

Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle? - Circular pool

The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Guests

How many ways can 5 guests sit down on 6 seats standing in a row? - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Pedestrian up-down hill

Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian? - Birthdate

Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?

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