# Examples for secondary school students - page 53

- Axial cut

The cone surface is 388.84 cm^{2}, the axial cut is an equilateral triangle. Find the cone volume. - Remuneration

Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received? - The city 3

The city has 22,000 residents. How long it is expected to have 25,000 residents if the average annual population growth is 1.4%? - Equation with abs value

How many solutions has the equation ? in the real numbers? - Krkonose CZ

Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t - Cube in sphere

The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere. - Regular quadrilateral pyramid

Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - Potatoes 6

The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, in the second hour he sold five-sixth of the remaining potatoes, and in the third hour he had sold the last 40kg of potatoes. How many kg of potatoes d - Ice cream

Annie likes much ice cream. In the shop are six kinds of ice cream. In how many ways she can buy ice cream to three scoop if each have a different flavor mound and the order of scoops doesn't matter? - Forces

Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - Hydrostatic force

What hydrostatic force is applied to an area of 30 cm^{2}in water at a depth of 20 m? (Water density is 1000 kg/m3) - Chairs

Determine the number of seats in the seventh row and ninth row, if 3rd row has 14 seats and in every next row of seats has five more than the previous row. - Difference AP

Calculate the difference of arithmetic progression if the sum of its first 19 members Sn = 8075 and the first member is a_{1}= 20 - Savings

Paul has a by half greater savings than half Stanley, but the same savings as Radek. Staney save 120 CZK less than Radek. What savings have 3 boys together? - Resistance

Determine the resistance of the bulb with current 200 mA and is in regular lamp (230V). - Equation

Equation ? has one root x_{1}= 8. Determine the coefficient b and the second root x_{2}. - Metals

In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals. - Apples in baskets

Determine how many apples are in baskets when in the first basket are 4 apples, and in any other is 29 apples more than the previous, and we have eight baskets. - Circle's chords

In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle. - Cone

The rotating cone volume is 9.42 cm^{3}, with a height 10 cm. What angle is between the side of the cone and its base?

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