# Examples for 9th grade - page 17

- EQL triangle

Calculate inradius and circumradius of equilateral triangle with side a=77 cm. - 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. - 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. - Q-Exam

If tg α = 0.9, Calculating sin α, cos α, cotg α . - 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? - 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} - Morse alphabet

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

Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9° - Sphere A2V

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

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

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

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

Calculate missing side in a triangle with sides 17 and 34 and area 275. - XY triangle

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

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