# Units - math word problems

- The largest

The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder? - The edge of a cube

How much does the edge of a cube of 54.9 cm^{3}measure? - Ducats

The king divided the ducats to his three sons in a ratio of 2: 5: 4. How many ducats the king divided them if the youngest received 260 ducats, which was the least of all sons. - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Surface of the cube

Find the surface of the cube that has volume 1/1m3 2/0.001 m^{3}3/8000 mm^{3} - Squares ratio

The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte - Cuboid and ratio

Find the dimensions of a cuboid having a volume of 810 cm^{3}if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5 - Five-gon

Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm. - Annulus

Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n. - 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? - 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? - Corona virus

Calculate an estimate of the percentage of GDP (Gross Domestic Product) declined due to the quarantine related to the corona COVID-19 virus that lasts for 2 months, during which time the economic activity is down by 80%. - Wall thickness

The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm^{3}. - What percentage

What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km - Self-oscillation period

The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s. - Tropics and polar zones

What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33' - Temperature 13

Work out the temperature after each change. The temperature starts at 6°C and falls by 13°C. The temperature starts at 2°C and falls by 8°C - Discounts 2

The local fitness center offers membership discounts for hospital employees. According to the membership brochure, you will receive a discount of 25% on a membership that normally costs $65 per month. How much will you pay for an annual membership if you - Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p - Liquid

How much liquid does the rotary cylinder tank hold with base diameter 1.2m and height 1.5m?

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