# Examples for 9th grade

#### Number of problems found: 2591

- Regular n-gon

Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm? - Flowerbed 2

Around the square flower bed in a park is sidewalk 2 m wide. The area of this sidewalk is 243 m^{2}. What is the area of the flowerbed? - Center of the cube

Center of the cube has distance 16 cm from each vertex. Calculate the volume V and surface area S of the cube. - Mom and daughter

Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter? - Tank diameter

A cylindrical tank has a volume of 60 hectoliters and is 2.5 meters deep. Calculate the tank diameter. - 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. - The gardener

The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy? - Percent chaining

Calculate 20% from 70% from 80 km - Right triangle

It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b - The ditch

Ditch with a cross-section of an isosceles trapezoid with bases 2m and 6m are deep 1.5m. How long is the slope of the ditch? - Scale

Cylinder was drawn in scale 2:1. How many times is the volume of the cylinder smaller in reality? - Three digits number

How many are three-digit integers such that in they no digit repeats? - Quadratic function

It is given a quadratic function y = -4x^{2}+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points. - Windbreak

A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree? - Tank No 8

Tank is filled by one inlet valve with a flow rate of 12 liters per second in 72 minutes. How long take the tank to fill, if we open half an hour after one more inlet? - Total displacement

Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back - Thales

Calculate the length of the Thales' circle described to right triangle with hypotenuse 44.2 cm. - Inscribed sphere

How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube? - Car

At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.) - Bus and Milan

The bus started from the village at speed 60 km/h. After one kilometer, when Milan came to bus stop on a motorcycle with grandmother. When they found that bus drove away he try to catch it. At the next stop, a distance of 3km caught up bus. How quickly ha

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