# Examples for 9th grade - page 14

- Pyramid

Pyramid has a base a = 9cm and height in v = 15 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges. - Parquet floor

Three workers laid parquet floor for 1.957 hour. The first one would do this work alone 5 hours, the second in 9 hours. For how many hours would fulfill this work the third worker, if he worked alone? - Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 6 so that it is divided into three parts in the ratio 3:2:5. Calculate the circumference of the triangle ABC. - Cylinder - h

Cylinder volume is 129 cm^{3.}Base radius is 3 cm. Calculate the height of the cylinder. - Slope

What is the slope of a line with an inclination 52°? - Stock market

Simon one day decided to invest € 88000 to the stock market. After six months he invested July 5 stock markets fell by 56%. Fortunately for Simon from July 5 5 to October 5 his shares have risen by 39%. Simon is then: ? - Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm^{2}and deviation angle of the side edges from the plane of the base is 60 degrees. - Prism

The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism? - Cyclists

Cyclist who rides at an average speed 17 km/h travels trip distance 14 min before the cyclist who rides at an average speed 15 km/h. What is the length of this cyclist trip(distance in km)? - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Division

Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 1:6:3. How many candies should each get if in bag were 210? - Track arc

Two straight tracks is in an angle 99°. They will join with circular arc with radius r=1292 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)? - Magnification of the square

If we increase the square side, increase the content of the 42 %. About what percentage was increased his sides? - House roof

The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m^{2}is needed to cover roof if roof pitch is 52° and we calculate 9% of waste, connections and overlapping of area roof? - Rotating cone II

Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm. - Playing cards

How many possible ways are to shuffle 7 playing cards? - The chord

Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°? - n-gon II

What is the side length of the regular 9-gon circumscribed circle of radius 13 cm? - Barrel 3

Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel? - Trigonometry

If you know that cos(α) = sin (-968°), what is the angle α?

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