# Grade - examples - page 9

- Homeless Dezider

Homeless Dežko has 9 coins in jacket: Calculate the value of its assets and calculate how many bottles of wine for 0.55 EUR can he buy. - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 38 cm and 55 cm long. - 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. - Washer

Washing machine drum wash at 55 RPM. Washing machine motor pulley has diameter 6 cm. What must be the diameter of the drum machine pulley when the motor is at 333 RPM? - Regular 5-gon

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

The cube has area of base 225 mm^{2}. Calculate the edge length, volume and area of its surface. - 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. - 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? - No. of divisors

How many different divisors has number ?? - 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? - Observer

The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - 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 €. - 7 heroes

9 heroes galloping on 9 horses behind. How many ways can sort them behind? - Textbooks

After check of textbooks found that every 10-th textbook should be withdrawn. Together 58 textbooks were withdrawn. How many textbooks were in stock before withdrawn and how many after withdrawn?

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