Volume - 9th grade (14y) - examples

  1. Scientific notation
    scientific Approximately 7.5x105 gallons of water flow over a waterfall each second. There are 8.6x104 seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day.
  2. Equilateral cylinder
    sphere_in_cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
  3. An oil
    valec2_13 An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
  4. Square prism
    lichob_2 Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
  5. Pool
    pool If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
  6. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 5951 cm3. Determine the length of the edges of a cube.
  7. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  8. Cuboid
    cuboid Cuboid with edge a=23 cm and body diagonal u=41 cm has volume V=13248 cm3. Calculate the length of the other edges.
  9. Pool
    swimming-pool The swimming pool is 10 m wide and 22 m long and 191 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
  10. 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 254 cm2.
  11. Transforming cuboid
    cube Cuboid with dimensions 10 cm, 17 and 17 cm is converted into a cube with the same volume. What is its edge length?
  12. Sphere
    1sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
  13. Pipes
    water_pipe Water pipe has a cross-section 1405 cm2. An hour has passed 756 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 15 hours if water flow same speed?
  14. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
  15. Tanks
    hasici Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
  16. Cuboid diagonal
    cube_2 Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
  17. Engineer Kažimír
    demagog_smer_1 The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri
  18. Sea water
    sea_1 Seawater contains about 4.7% salt. How many dm3 of distilled water we must pour into 39 dm3 of sea water to get water with 1.5% salt?
  19. Barrel of oil
    dieselbarrel Barrel of oil weighs 253 kg. When it mold 43% oil, weighed 159 kg. What is the mass of the empty barrel?
  20. Sand pile
    sandpile_1 Auto sprinkled with sand to approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the sand c

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