Examples for 9th grade - page 14
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 cm3. Base radius is 3 cm. Calculate the height of the cylinder.
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 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
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?
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.
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 m2 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?
If you know that cos(α) = sin (-968°), what is the angle α?