# Examples for 8th grade - page 4

- Square

Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Rectangle

The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 18 km/h, the second at average speed 24 km/h. Determine the distance between them after 30 minutes cycling. - Cube diagonal

Determine length of the cube diagonal with edge 55 dm. - Z9-I-4

Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi - River

From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river. - Discount

Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 72 USD. Determine the original price of sweater. - Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm^{2.}What scale is the city plan? - Gimli Glider

Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2080 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate - Short cut

Imagine that you are going to the friend. That path has a length 330 meters. Then turn doprava and go another 840 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 cm^{2.}Calculate the volume of a cone. - Regular 5-gon

Calculate area of the regular pentagon with side 11 cm. - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 15 cm and 27 cm long. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm^{2.} - Logs

Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm? - Right triangle Alef

The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs. - Sphere

Surface of the sphere is 2260 cm^{2,}weight is 52.2 kg. What is its density? - Motion2

Cyclist started out of town at 20 km/h. After 0.6 hours car started behind him in the same direction and caught up with him for 52 minutes. How fast and how long went car from the city to caught cyclist? - ŽSR

Calculate fixed annual personnel costs of operating monorail line 106 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 3-shift operation. Consider the average salary of the employee 847 €. - Rhombus ABCD

Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD.

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