# Examples for 9th grade - page 65

- Chord 2

Point A has distance 13 cm from the center of the circle with radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle. - Flowerbed

Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m^{2}=. - Axial section

Axial section of the cylinder has a diagonal 18 cm. The size of the shell and the base surface are in the ratio 2:3. Calculate the volume and surface area of this cylinder. - Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm^{2.} - Right triangle

Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC. - Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC. - Two months

Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies? - 10 pieces

How to divide the circle into 10 parts (geometrically)? - Metal alloy

What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel? - Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal. - Scouts

Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type? - Max - cone

From the iron bar (shape = prism) with dimensions 8.4 cm, 5.7 cm, 10.7 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste. - Sphere

Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere. - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - Triangle midpoints

Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC. - Concentric circles

In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord. - Circle and hexagon

Calculate the radius of a circle whose circumference is 6.8 cm longer than the circumference of the inscribed regular hexagon. - 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. - Otto and Joachim

Otto and Joachim go through the woods. After some time Otto tire and make 15 minutes stop. Joachim meanwhile continues at 5 km/h. Otto when he set off again, first running speed of 7 km/h, but it keep only 30 sec and 1 minute must continue at 3 km/h. This. - Enterprise and wages

The enterprise operates a total 159 workers and their average salary is M dollars. If the company has hire an additional 21 employees whose average wage would be the S dollars, would reduce the overall average salary in the company of 2%. Calculate the v

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