# Examples for 9th grade - page 16

- Sector

The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes. - MO - triangles

On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se - Pairs

At the table sit 8 people, 4 on one side and 4 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit? - Q-Exam

If tg α = 0.9, Calculating sin α, cos α, cotg α . - Block

Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9° - Cone and the ratio

Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface. - Cardboard box

We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal - Morse alphabet

Calculate how many words of Morse code to create compiling commas and dots in the words of one to four characters. - Sphere A2V

Surface of the sphere is 296 cm^{2.}What is its volume? - Steamship

Between the two ports on the river is going steamship. The journey there and back takes 8:42. Downstream steamship traveling at 20 km/h, upstream 9 km/h. What is the distance between the ports? - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - Trapezoid - diagonal

Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm^{2.}What is the area of the trapezoid? - Scrap

From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product? - Leveling

Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 15 m^{2}to the "height" 6 mm if consumtion is 1.5 kg per square meter and millimeter thickness. - Blueberries

Marie earns 3 liters of blueberries for 3.4 hours, Peter 2.4 liters for 2.9 hours. How long have earns together one liter? - Three workers

Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 11 days, B together with C for 15 days, A together with C for 24 days. How long it would take to complete the task every one of them alone? How long it would. - Triangle angles

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

The rectangle shaped field with dimensions 889 m and 1336 m harvested last year was 6235 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 3 m parallel to the side of the field 1336 m, where. - Amazing number

An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.

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