# Examples for 9th grade - page 6

- MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Railways

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

The tale of the Seven Ravens were seven brothers, each of whom was born exactly 1.5 years after the previous one. When the eldest of the brothers was 4-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur - Radians

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

Calculate the area of a right triangle whose longer leg is 9 mm shorter than the hypotenuse and 4 mm longer than the shorter leg. - 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? - 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. - Sand pile

Auto sprinkled with sand to approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the sand c - 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 ?. - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has maximum area. - Z9–I–1

In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir - 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? - Lathe

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

Calculate perimeter of the circle described by a triangle with sides 418, 59, 430. - Daily average

Calculate the average temperature during the day, when 14 hours was 20 °C and 10 hours was 15 °C. - Rhombus and inscribed

Rhombus has side a = 72 cm, the radius of the inscribed circle is r = 10 cm. Calculate the length of its two diagonals. - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 23 cm and t_{b}=14 cm. - Rectangle - sides ratio

Calculate area of rectangle whose sides are in ratio 1:7 and perimeter is 735. - Pediatrician

Pediatrician this month of 21 working days takes 3 days holidays. What is the probability that on Monday will be at work? - VAT

John paid 1000 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%.

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