# Examples for 9th grade - page 17

- Mystery of stereometrie

Two regular tetrahedrons have surfaces 56 cm^{2}and 126 cm^{2.}In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Divisibility

Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2. - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - Drunk man

Drunkman has 2.1‰ of alcohol in the blood. How many grams of alcohol has in blood, if he have 6 kg of blood? - Lid

What is the weight of concrete cover (lid) to round shape well with a diameter 1.3 m, if the thickness of the cover is 15 cm? 1 m^{3}of concrete weighs 2190 kg. - Sea

How far can you see from the ship's mast, whose peak is at 11 meters above sea level? (Earth's radius is 6370 km). - Glass of juice

Glass of juice shaped cylinder 16 cm height and base diameter of 10 cm is filled with juice so that the level is 3 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow. - Spherical segment

Spherical segment with height h=8 has a volume V=294. Calculate the radius of the sphere of which is cut this segment. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=13 cm, v_{b}=17 cm and side b is 5 cm shorter than side a. - Electronics: Resistors in parallel

From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R_{1}= 8kΩ a R_{2}= 18kΩ - 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 - Nine-gon

Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 20 cm. - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 814 km away? Assume the earth to be a smooth sphere with radius 6378.1 km. - Pit

Pit has shape of a truncated pyramid with rectangular bases and is 2.8 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 0.3 l of green colour. How many liters of paint is needed when w - AVG of INT

What is the average of the integers from 7 throuht 15 inclusive? - Cyclist

A cyclist is moving at 26 km/h and follow pedestrian who is walking at speed 7 km/h. Walker has an advantage 13 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. - Plasticine ball

Plasticine balls have radius r_{1}=100 mm, r_{2}=48 cm. For these balls are molded one big ball. Calculate the radius r of the resulting ball. - Car factory

Carmaker now produce 4 cars a day more than last year, so the production of 413448 cars will save just one full working day. How many working days needed to manufacture 413448 cars last year? - Lock

Combination lock will open when the right choice of 4 numbers (from 1 to 14 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?

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