# Examples for 9th grade

#### Number of problems found: 2621

- Volume ratio

Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - Hiking trail

The newly built hiking trail leads 25% through the field, 3/8 of the trail leads through the forest and the remaining 9 km along the river. How long is the train? - Copper Cu wire

Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic. - Art school

Every fifth pupil 9A goes to art school. How many percent of pupils in class 9A go to art school? - Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place. - Air draft

The numbers 1,2,3,4,5 are written on five tickets on the table. Air draft randomly shuffled the tickets and composed a 5-digit number from them. What is the probability that he passed: and, the largest possible number b, the smallest possible number c, a - At the

At the presentation of the travelers came three times as many men than women. When eight men left with their partners, there were five times more men than women at the presentation. How many were men and women originally? - 2 cyclists and car

One cyclist rides at a constant speed over a bridge. It is 100 meters long. When he is 40 meters behind him, he meets an oncoming cyclist who is riding at the same speed. The car travels along the bridge in the same direction as the first cyclist at a spe - The half life

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives? - Twelve ties

The price of 12 ties before the discount was the same as 15 ties after discount. Calculate the price of 1 tie after discount, if you know that the discount price of one tie fell by 40 CZK? - Diggers

Eight diggers will do the job in 85 hours. After 21 hours, 3 diggers had to leave. How many hours will the work be done? - Sweets, candy

Grandfather gave out sweets to four children. At the last moment, two more children came, so in order to have them all the same, each of the four children would receive four candies less than they would have received if they had not. How much did my grand - Receiving heat

How many degrees Celsius was an iron cylinder weighing 300 g heated in a water bath if it received heat of 7.2 kJ? (specific heat capacity of iron c = 0.46kJ/kg / ºC) - Five letters

How many ways can five letters be arranged? - Parallelogram

Find the perimeter of the parallelogram, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A. - Five tractors

Five tractors plow the fields in 4.8 hours. How long will it take to plow the field when, after an hour and a half of work, two tractor drivers have been called up for another task? - Two gardens

The total area of the two gardens is 864 m^{2}. The first garden is 60 m^{2}smaller than three times the second garden. What is the area of each garden? - Baking muffins

Aunt Polly is baking muffins at a speed of 4 muffins per minute. Tom comes into the kitchen when Aunt Polly has 12 muffins, and begins to eat these muffins at a speed of 6 muffins per minute. When he finally leaves the kitchen, there are 4 muffins at the - Columns of two and three

When students in one class stand in columns of two there is none left. When he stands in columns of three, there is one student left. There are 5 more double columns than three columns. How many students are in the class? - Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?

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