Examples for 9th grade - page 14
- 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: ?
- Cylinder - h
Cylinder volume is 129 cm3. Base radius is 3 cm. Calculate the height of the cylinder.
Vojta left the house at three o'clockat 4 km/h. After half hour later went from the same place Filip by bicycle at speed 25 km/h. How long take Tilip to catch up Vojta and how far from the house?
A passenger train traveled for 4 hours 136 km. 2.7 hours after its departure started fast train and caught it on 324 km. How many km/h is different its average speeds?
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?
- Wire D
Wire length 5 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
- 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)?
- Square grid
Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
- Playing cards
How many possible ways are to shuffle 7 playing cards?
Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 16 cm and a height v=10 cm.
- 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.
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?
- 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?
- Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
- Rotating cone II
Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm.
Calculate the length of the belt on pulleys with diameters of 162 mm and 454 mm at shaft distance 425 mm.
- Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
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)?
- Right triangle
Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm.
The boys from scout group traveled 3 days distance 105 km. Every day walked 1.3 km less than the previous day. How many kilometers scouts walked in the first day?