Units - math word problems

  1. The largest
    cylinder_in_cube The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder?
  2. The edge of a cube
    cubes How much does the edge of a cube of 54.9 cm3 measure?
  3. Ducats
    dukat 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.
  4. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  5. Surface of the cube
    cubes3 Find the surface of the cube that has volume 1/1m3 2/0.001 m3 3/8000 mm3
  6. Squares ratio
    squares2 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
  7. Cuboid and ratio
    cuboid_2 Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
  8. Five-gon
    5gon_diagonal Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  9. Annulus
    annulus_inscribed_circles 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.
  10. Two gardens
    garden The total area of the two gardens is 864 m2. The first garden is 60 m2 smaller than three times the second garden. What is the area of each garden?
  11. Twelve ties
    kravata 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?
  12. Corona virus
    covid19 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%.
  13. Wall thickness
    sphere_Nickel 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/cm3.
  14. What percentage
    astronaut 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
  15. Self-oscillation period
    lambda 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.
  16. Tropics and polar zones
    circles_on_Earth 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'
  17. Temperature 13
    teplomer 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
  18. Discounts 2
    sale 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
  19. Tetrahedral pyramid 8
    pyramid_4s 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
  20. Liquid
    valec How much liquid does the rotary cylinder tank hold with base diameter 1.2m and height 1.5m?

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