# Examples for 9th grade - page 28

- 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. - Carpenter

From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off? - 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 - 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 dm^{2}. - 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. - 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. - Quadrangular prism

The quadrangular prism has a volume 648 cm^{3}. 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? - 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 - 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. - 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? - 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/s^{2}. - 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? - 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. - 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. - Reciprocal

What is the reciprocal of the sum of the reciprocals of 4 and 9? - Quadratic equation

Solve quadratic equation: 2x^{2}-58x+396=0 - Trapezoid

Area of trapezoid is 135 cm^{2}. Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation... - Iron fence

One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m^{3}. - Two cars

From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what.

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