# Examples for 8th grade - page 4

- Short cut

Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm^{2.}Calculate the volume of a cone. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm^{2.} - Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm^{2.}What scale is the city plan? - River

From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river. - Cube diagonal

Determine length of the cube diagonal with edge 33 km. - Discount

Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 70 USD. Determine the original price of sweater. - Regular 5-gon

Calculate area of the regular pentagon with side 7 cm. - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 2 cm and 6 cm long. - Logs

Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm? - Right triangle Alef

The area of a right triangle is 294 cm^{2,}the hypotenuse is 35 cm long. Determine the lengths of the legs. - Sphere

Surface of the sphere is 2820 cm^{2,}weight is 71 kg. What is its density? - Square and circles

Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Motion2

Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist? - Chickens and rabbits

In the yard were chickens and rabbits. They had 31 heads and 94 legs. How many chickens and how many rabbits was in the yard? - No. of divisors

How many different divisors has number ?? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - Rectangle

In rectangle with sides 3 and 10 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - ŽSR

Calculate fixed annual personnel costs of operating monorail line 118 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 4-shift operation. Consider the average salary of the employee 885 €. - Rhombus ABCD

Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD.

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