# Examples for 9th grade - page 17

- Magnification of the square

If we increase the square side, increase the content of the 80 %. About what percentage was increased his sides? - 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. - Scouts

The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day? - 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 - Sphere A2V

Surface of the sphere is 241 mm^{2}. What is its volume? - 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} - 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? - Tanker

An oil tanker can be emptied by the first pump in 4.9 hours. Second pump can empty an tanker in 8 hours. If the first pump started at 4:00 and second 1.4 hour later, at what time will the tanker be empty? - 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. - Morse alphabet

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

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

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

Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9° - 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. - 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. - 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? - XY triangle

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

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