# Grade - examples - page 59

- Squaring the Circle

Calculating side of the square with the same area as the circle of radius 18. - 3sides prism

The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism. - Skier

At this point, the first skier lead 20 km before the second skier and travels at a constant speed 19 km/h. The second skier rides at 24 km/h. How long take him to catch up the first? - The professor's birthday

Professor of mathematics had 57 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc - Pool coating

How many pieces of tiles 25 cm × 15 cm need to coat the bottom and side walls of the pool with bottom dimensions 30 m × 5 m, if the pool can fit up to 271500 liters of water? - Square side

Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0. - Triangle

Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33. - ISO Triangle V2

Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle. - Carbon dioxide

Calculate how many grams of oxygen are in 50 g of carbon dioxide CO_{2}. Relative atomic mass of oxygen is 16 and of carbon is 12. - Bricks

Openings in perforated bricks occupy 10% and brick has dimensions 30 cm, 15 cm and 7.5 cm. Calculate a) the weight of a perforated bricks, if you know that the density of the full brick material is p = 1800 kg/m^{3}(1.8 kg/dm^{3}) b) the number of perforated. - Again saw

From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter? - Resistors

Two resistors connected in series give the resulting resistance 216Ω and 48Ω in parallel. Determine the resistance of this resistors. - School trip

6.A class went on a trip. Train ticket cost 6 euros, cable car ticket 6 euro. How many euros must pay classroom teacher for 23 students? - Forest nursery

In Forest nursery plant one pine to 1.9 m^{2}. Calculate how many plants are planting in area 362 acres. - Pumps 3

Two pumps of the same power fill the garden pool for 10 hours. How many of these pumps would have to use if we want to shorten the filling of the pool to four hours? - Thermometer

The thermometer showed -3°C at morning. Then temperature was increased by 1°C again increased by 1°C and then decreased by 1°C and then decreased by 4°C. Which terminal temperature thermometer shows? - Triangle

Prove whether you can construct a triangle ABC, if a=9 cm, b=10 cm, c=4 cm. - Similarity of squares

The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ? - Gon functions

Decide which of the numbers (values of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1. - Pennies

800 pennies have the same value as 100 ducats. 100 pennies have the same value as 250 tolars. How many ducats has the same value as 100 tolars?

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