# Examples for 9th grade - page 17

- Triangle angles

The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles. - Shooter

The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot? - Compass

What angle are between directions WSW (WestSouthWest) and SSE (SouthSouthEast) on the compass? - Hollow sphere

Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m^{3} - XY triangle

Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y. - Coin and die

Flip a coin and then roll a six-sided die. How many possible combinations are there? - 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. - Pumps

Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo - 3y inflation

Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll. - Slope of the pool

Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 0.85 m (for children) and depth at end is 1.73 m (for swimmers). Slope express as percentage and as angle in degrees. - 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. - 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. - Drunk man

Drunkman has 1.6‰ of alcohol in the blood. How many grams of alcohol has in blood, if he have 7 kg of blood? - Road

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

Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m^{2}for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin - 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. - Glass of juice

Glass of juice shaped cylinder 16 cm height and base diameter of 7 cm is filled with juice so that the level is 4 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow. - 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).

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