# Examples for 9th grade

- Diagonal intersect

isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles? - Milk

There were 22 liters of milk in three containers. There was 6 liters more in the first container than in the second. After pouring 5 liters from the first container into the third container, the same quantity of milk is in the second and third container. - Average monthly salary

A total of 10 teachers work at one small school in Moravia. The monthly salary of each is 21,500 CZK or 21,800 CZK or 22,500 CZK according to their education and age. The average monthly salary for this school's teacher is 21 850 CZK. How many teachers of - A cloth

There are flower cloth 495 meters, white cloth 330 meters. What is the percentage of white cloth? How much is white cloth less than flower cloth? - Axial section of the cone

The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square. - Cone side

Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side. - The Indian tent

The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire? - Unknown number

15% of the unknown number is 18 less than 21% of the same number. What is the unknown number? - The product

The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number - Pool

How many hl of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m^{2}? - Scholarship

The annual scholarship of the best student and second-best student in the class is 3500 euros in total. The best student scholarship in 8 months is the same as the second-best student scholar in the class for the whole year. How big is the annual scholars - 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 - Cylinder

The 1.8m cylinder contains 2000 liters of water. What area (in dm^{2}) of this container is the water? - Panel house

The construction company has two groups of workers. Group A has more members than B. Panel house was insulated by group A in 10 days. The same block of flats was insulated together in 6 days. How many days would group B block insulate? - Regular hexagonal pyramid

Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture. - Octagonal pyramid

Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°. - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´. - Pairs of socks

Ferdinand has twelve pairs of socks, one sock is leaky. What is the probability of putting on a leaky sock? - Uboid volume

Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm² - Hexagonal pyramid

Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.

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