# Examples for 8th grade - page 19

- Divisibility

Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16. - Mystery of stereometrie

Two regular tetrahedrons have surfaces 88 cm^{2}and 198 cm^{2.}In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Road

Average climb of the road is given by ratio 1:15. By what angle road average climb? - Spherical segment

Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment. - Lid

What is the weight of concrete cover (lid) to round shape well with a diameter 1.8 m, if the thickness of the cover is 11 cm? 1 m^{3}of concrete weighs 2190 kg. - Nine-gon

Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm. - Sea

How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km). - Water inlets

Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long take to fill full tank if we open one more such valve half an hour after? - Pit

Pit has shape of a truncated pyramid with rectangular bases and is 3.5 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.8 l of green colour. How many liters of paint is needed when w - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km. - Purchase

Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at the - Lines

Five bus lines runs at intervals 3, 6, 9, 12, 15 minutes. In the morning, suddenly start at 4:00. After how many minutes the bus lines meet again? - Electronics: Resistors in parallel

From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R_{1}= 2Ω a R_{2}= 15Ω - AVG of INT

What is the average of the integers from 9 throuht 52 inclusive? - Lock

Combination lock will open when the right choice of 3 numbers (from 1 to 25 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately? - Cyclist

A cyclist is moving at 35 km/h and follow pedestrian who is walking at speed 4 km/h. Walker has an advantage 19 km. How long take cyclist to catch up with him? - Train from Prague

First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km. - Hiker

Hiker went half of trip the first day, the third of trip the second day and remaines 15 km. How long trip he planned? - Fertilizer

Mr. Gherkin use for fertilization 8% solution of fertilizer. 4 liters of it still left. How much water must be added to the solution to make only 4% solution? - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille?

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