Body volume - problems

  1. Water block
    cukr_8 A block with a 50 cm2 base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
  2. 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%?
  3. Rainfall
    rain_6 A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
  4. Conical area
    cones_2 A right angled triangle has sides a=11 and b=10 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
  5. Quadrangular pyramid
    komoly Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
  6. Cylinder horizontally
    CylindricalSegment_1000 The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
  7. Three cubes
    cubes3 The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
  8. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 6598 cm3. Determine the length of the edges of a cube.
  9. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
  10. Cuboid
    cuboid Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
  11. Cuboid
    cuboid_1 The cuboid has a surface area 3380 cm2, the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid.
  12. Pool
    swimming-pool The swimming pool is 4 m wide and 20 m long and 156 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
  13. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  14. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
  15. Transforming cuboid
    cube Cuboid with dimensions 5 cm, 14 and 17 cm is converted into a cube with the same volume. What is its edge length?
  16. Tereza
    cube The cube has area of base 64 mm2. Calculate the edge length, volume and area of its surface.
  17. Sphere
    1sphere Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
  18. Tanks
    hasici Fire tank has cuboid shape with a rectangular floor measuring 11 m × 14.3 m. Water depth is 1.3 m. Water was pumped from the tank into barrels with a capacity of 3.9 hl. How many barrels were used, if the water level in the tank fallen 3 cm? Wri
  19. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much?
  20. Rainfall
    storm Annual rainfall in our country are an average of 854 mm. How many m3 of water rains on average per hectare?

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