Percentages + body volume - math problems

  1. Kostka
    sphere_in_cube Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
  2. Triangular prism
    hranol3b The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
  3. The ball
    sphere4 The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
  4. Sphere radius
    SpheresDiff The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
  5. Pyramid cut
    ihlan_rez We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
  6. Hectoliters
    sudy_4 How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
  7. Cube into sphere
    cube_sphere_in The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
  8. Inscribed sphere
    cubes2_7 How many percents of the cube volume takes the sphere inscribed into it?
  9. Cube edges
    cubes3_3 If the edge length of the cube increases by 50%, how does the volume of this cube increase?
  10. Water tank
    nadrz_13 A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
  11. Volume and body diagonal
    kvader11_11 Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
  12. Volume increase
    basen_6 How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
  13. Sugar cubes
    cukr_5 The glass has 600 ml of tea, which represents 80% of the volume of the glass. If you put twenty regular sugar cubes of 2 cm in the tea, how many ml of tea are poured?
  14. Ice and water
    ice_playground We want to cover rectangular rink with dimensions of 55 m and 25 m with 4cm thick layer of ice. How many liters of water we need if after freezing water increases its volume by 10%?
  15. Fuel economy
    car1_4 How many kilometers is sufficient petrol in the cylinder fuel tank with a diameter 40 cm and the base of tank length 1 m, when it is filled to 60% and if the car consume 15 liters per 100 km?
  16. Cuboid enlargement
    cubes_12 By how many percent increases the volume of cuboid if its every dimension increases by 30%?
  17. Vintner
    wine How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number
  18. Inscribed sphere
    ball-in-cube How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
  19. The tent
    stan The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
  20. Roof 8
    veza_1 How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.

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