Examples for 9th grade - page 29

Angles in triangle
The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
Diamond ABCD
In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.
Racing track
On the racing track circling three cars. The first passes one circuit for 8 seconds, the second for 20 seconds and a third for 8 seconds. a) Calculate number of seconds since the start to catch all three cars together for the first time again across the s
Carpenter
From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
Ice cream in cone
In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone.
Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm².
Cross-country competition
Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B?
Quadrangular prism
The quadrangular prism has a volume 648 cm³. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
Car
The driver of a car is to get to 608 km distant city. From atlas found that 162 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 116 km/h. Calculate how many hours it will t
Two diggers
There are two diggers. One digger digs a pit 46 hours second gidding 2 times faster. a) how long took to dig a pit second digger b) how long took dig together
Tourist Jirka
Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
Reciprocal
What is the reciprocal of the sum of the reciprocals of 4 and 9?
Mountain railway
Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
Bomber
Bomber flies 10 km at 600 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s².
Sphere cuts
At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
Trapezoid
Area of trapezoid is 135 cm². Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
Grandson and granddad
Grandson with grandpa they counted how many years have together. Their product is 365. How many years is the sum of their years.

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