Volume - 8th grade (13y) - examples

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  1. 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 =?
  2. Three cubes
    cubes3_2 The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
  3. Container
    valec2_5 The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
  4. Pool
    pool If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately?
  5. 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.
  6. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
  7. 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.
  8. 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.
  9. 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.
  10. Sphere
    1sphere Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
  11. 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
  12. 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?
  13. Density - simple example
    mercury Material of density of 1278 kg/m3 occupies a container volume of 80 cm3. What is its mass?
  14. Cuboid diagonal
    cube_2 Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.
  15. Alcohol
    no_alcohol How many 46% alcohol we need to pour into 3 liters 63% alcohol to get p3% of the alcohol? How many 52% alcohol we get?
  16. 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
  17. Water
    tanks Mix 61 l of water with temperature of 48 °C, 58 l warm of 57 °C and 47 l water of 39 °C. What is the temperature of the mixed water immediately after mixing?
  18. Cone
    cones Circular cone of height 16 cm and volume 5024 cm3 is at third of the height (measured from the bottom) cut plane parallel to base. Calculate the radius and circumference of the circular cut.
  19. Barrel of oil
    dieselbarrel Barrel of oil weighs 238 kg. When it mold 20% oil, weighed 196 kg. What is the mass of the empty barrel?
  20. Cu thief
    trolleywire_1 The thief stole 121 meters copper wire with cross-section area of 101 mm2. Calculate how much money gets in the scrap redemption, if redeemed copper for 5.5 eur/kg? The density of copper is 8.96 t/m3.

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